Aeration does a lot of great things for your pond, and for your fish, so it is far from a waste. However, the answer to your question is no, aeration will not help prevent or manage filamentous algae populations. Don't take my word for it, search the scientific literature available from thousands of journals with millions of publications. Try for example the Journal of Aquatic Plant Management, the preeminent journal on the subject of aquatic vegetation management. I have never seen a single scientifically published study that demonstrates aerations helps control filamentous algae in any way.

However, pond and lake management companies, trade magazines, aeration companies, and popular articles constantly state that aeration helps prevent or control filamentous algae. It is a sales gimmick, and I believe that it has been used so long in the industry that a lot of pond and lake management professionals BELIEVE it is true. However, people that buy into this gimmick often turn to Extension seeking facts when aeration fails. Next time someone offers you a service, demand they show you a peer-reviewed, scientific research article published in a reputable journal, not a magazine or sales brochure. If they can't, then don't pay for the service.

I am not sure, because it goes way back before my time, but I think this myth has roots in early studies on pond and lake aeration and how it influences phytoplankton communities. Yes phytoplankton in another name for algae, but these are very different from filamentous algae. Phytoplankton are single celled, microscopic algae that are freely floating in the water. They are what gives the water a slightly green tint. If you increase the population of these phytoplankton to high densities, they can act as a natural "pond dye" in the fact that they function the same as dyes by blocking sun from reaching the bottom where vascular plants and filamentous algae start. If the phytoplankton blocks sun from reaching the bottom the plants and filamentous algae die-off before they can get started. However, phytoplankton at high densities are not without their own problems, such as aesthetically unpleasing water color, potential fish die-off due to low dissolved oxygen from rapid algae die-off, and cyanobacteria (blue-green algae) produce toxins that can harm wildlife, fish, pets, and can become dominant in the phytoplankton community.  

Aeration can help create a phytoplankton bloom in certain situations, and I believe this has become widely misinterpreted as a means to control filamentous algae. However, in other situations, it can reduce the phytoplankton population, and believe this has become widely misinterpreted as a means to control phytoplankton blooms. So now aeration is a magical cure all for all algae types, but it couldn't be further from the truth because every pond or lake responds to aeration differently. Could aeration decrease filamentous algae in some situations? Absolutely, but it is also more likely make the problem worse. Again it all depends on the characteristics of the pond. It is however, not a reliable management method for any form of algae. Take the abstract below from a peer-reviewed, scientific research article published in a reputable journal in 1973 (one of those early aeration studies). It demonstrates the two spectrums that could result due to the addition of aeration.

EFFECTS OF ARTIFICIAL AERATION ON THE CHEMISTRY AND ALGAE OF TWO MICHIGAN LAKES

Water Resources Research 9(3):624-647. 1973. SFA 18(4).

Two lakes were artificially aerated by using compressed air. Section Four Lake, an unproductive lake, was completely mixed, whereas Hemlock Lake, a eutrophic lake, had its hypolimnion aerated but thermal stratification maintained. Chemical and algal changes in Section Four Lake during destratification were not great. Although phytoplanktonic production potentials increased during mixing, the phytoplankton standing crop appeared to decline slightly, possibly due to the increased mixing depth and turbidity. Hemlock Lake hypolimnetic anoxia and conditions associated with it were eliminated during aeration, The lake gradually destratified during aeration due to leaks in the aeration tower. These leaks also released nutrient rich water into the epilimnion, which promoted algal growth. | IN ORDER TO DETERMINE THE EFFECT OF ARTIFICIAL AERATION IN LAKES, AN UNPRODUCTIVE HARD WATER LAKE (SECTION FOUR LAKE) AND AN EUTROPHIC LAKE (HEMLOCK LAKE) WERE ARTIFICALLY AERATED USING COMPRESSED AIR. SECTION FOUR LAKE WAS COMPLETELY MIXED WHEREAS HEMLOCK LAKE HAD ITS HYPOLIMNION AERATED BUT THERMAL STRATIFICATION MAINTAINED. WATER SAMPLES WERE COLLECTED WITH A PVC VAN DORN SAMPLER AND DETERMINATIONS WERE MADE FOR DISSOLVED OXYGEN, CARBON DIOXIDE, PH, TOTAL ALKALINITY, CONDUCTIVITY, TOTAL DISSOLVED ORGANIC CARBON, TOTAL PARTICULATE ORGANIC CARBON, CA, MG, K, AND NA. TOTAL CARBON CONTENT OF THE SEDIMENT WAS ALSO MEASURED. FOAM SAMPLES WERE ANALYZED FOR TOTAL P, N, AND HG. PRIMARY PRODUCTIVITY ESTIMATES WERE MADE, AND PHYTOPLANKTON AND PERIPHYTON SAMPLES WERE ANALYZED. CHEMICAL AND ALGAL CHANGES IN SECTION FOUR LAKE DURING DESTRATIFICATION WERE NOT GREAT. ALTHOUGH PHYTOPLANKTONIC PRODUCTION POTENTIALS INCREASED DURING MIXING, THE PHYTOPLANKTON STANDING CROP APPEARED TO DECLINE SLIGHTLY, POSSIBLY DUE TO THE INCREASED MIXING DEPTH AND TURBIDITY. HEMLOCK LAKE HYPOLIMNETIC ANOXIA AND CONDITIONS ASSOCIATED WITH IT WERE ELIMINATED DURING AERATION. THE LAKE GRADUALLY DESTRATIFIED DURING AERATION DUE TO LEAKS IN THE AERATION TOWER. THESE LEAKS ALSO RELEASED NUTRIENT RICH WATER INTO THE EPILIMNION, WHICH PROMOTED ALGAL GROWTH.

Most Extension specialist and researchers will tell you that nutrient management is the best way to manage pond algae.  First use a tank mix of diquat and copper based algaecide, a mixture that has proven to provide better control of algae than either chemical alone, to kill off any existing algae.​ These are contact herbicides that quickly and can create massive amounts of rotting vegetation. Treat no more than 25 to 30% of the pond area at a time to avoid low dissolved oxygen fish kills due to rotting vegetation. Wait 7-10 days before treating the next 25%, and continue this process until the entire pond is treated. Follow spot applications may be necessary for any algae that is missed during the initial treatments.

Next, let's discuss how to prevent it from coming back as bad or very quickly. The number one reason for algae problems to develop in ponds is too much phosphorus in the water. When you kill the algae it releases all of the nutrients contained in it, including the phosphorus, back into the water. In order to prevent it from coming back as quickly, apply a phosphorous binder to each 25% of the pond around 5 days after you treat it. This will take the phosphorous out of the water column and lock it in the sediment where it can't be utilized by the algae again. This will help prevent it from becoming a problem again. Repeated treatments may be used if necessary. There are many phosphorus binding products, such as Phoslock.  

After binding the phosphorous, you may want to use sludge reducing products containing natural bacteria that eliminate the organic material in the pond muck that is the source for a large amount of the nutrients filamentous algae utilize. There are many manufacturers and products, such as NT-Max. The last preventative option is to use a water column clarifier the day following the diquat + copper treatment. These clarifiers are liquid bacterial blends that fixate nitrogen and phosphorus at faster than normal rates to clarify water. This way you get herbicide treatment and nutrient removal all in one step.