Do you mean separating the beds completely form the ground by either a solid surface or an air space?
If so, this is certainly possible, but understand this will be much more like container gardening. The biggest drawbacks to growing vegetables in containers are that root space is limited, irrigation will be more frequent, and it is often harder to maintain even soil moisture.
If you just mean that you will raise the sides of the beds, roots will still be able to go deep, but there may still be the possibility of some tree roots coming up. In-ground, tall raised beds will dry out a little faster, but the drainage should be very good.
Also high beds mean less bending over, which can be easier on back strain.