Hi Katherine, Thanks for the question.

Although there is a lot of information on Alfalfa meal/pellets and alfalfa hay, there does not seem to be a lot of well researched information on their use as amendments. There are a lot of claims without sufficient support.  Alfalfa meal is sold as a rather quick acting fertilizer. A soil test (Home | MSU Soil Test) is recommended to help determine what your soil may need. Surveying the various literature here is what was found:

Alfalfa Hay:

Advantages:

• It is rich in nitrogen, calcium, magnesium and other nutrients.
• It’s acts like most organic mulches returning its nutrients back to the soil like a slow-release fertilizer.
• It can help in water retention and improve soil structure.
• When used as mulch, it helps with weed control and moisture retention.

Disadvantages:

• If the hay dries out on the ground surface, the nitrogen may escape into the air and not be available to the crop. 
• May be expensive compared to other organic mulches.

Alfalfa Meal 

Advantages:

• Organic material in the soil increases and suppling nutrients to the roots of plants. 
• Decomposition of organic matter is enhanced by the nitrogen content. Its high nitrogen content aids the decomposition of other organic matter.
• It contains the growth stimulant Triacontanol.
• It helps with water retention and soil tilth.
• It decomposes fast.

Disadvantages:

• It might not be as readily available or as cost-effective than alfalfa hay.
• More processed than alfalfa hay.

I hope this is helpful.