Hello in Florida- 

First I need to ask if the tree is already in place and you are thinking of putting a drainage pipe in its root zone or if you are thinking of planting a tree above an existing drainage line.

If the tree is already growing (32' canopy, etc.) digging  a trench 3' deep in it's root zone will damage the stability and health of the tree.  This might result in a shorter life span.

If the situation is that you are thinking of planting a tree over a pipe, you should know that your live oak tree will tend to keep most of it's roots in a layer that is above that 3' line- especially if there is a high water table. Even it has a deeper tap root in it's younger years, as it ages, that tap root will become less important with most of the tree's root system provided by the the lateral roots.

If a large mature tree is blown over it may disturb the soil around and above the drain pipe that might result in damage, and the likelihood of this happening is increased in the first scenario if you are trenching across the roots to install a drainline.

Also, if there is any chance that the pipe will not maintain tight seals that will prevent leakage, then perhaps you should reconsider.  The tree will not- does not- break the pipe open "looking for water". If any cracks develop in the pipe such that water seeps out of the pipe below the roots of the tree, the tree's roots will seek out the moisture in the soil and may exploit any cracks in the pipe by growing into the pipe.

  I hope this helps make your decision.