Hi Dave.
Not only is it possible,but it is a very enjoyable trip in itself.I just brought my privilege 39 up the TennTom to the middle Tennessee area.You will need to know your mast height off the water.I can tell you the lowest clearance from Kentucky Lake to Mobile Bay is 48Ft.Most are 52ft+.This will vary some with water level which is usually marked at each bridge.Excellent reference is Nitty Gritty by Fred Meyers.Three things to look out for are floating logs or trees (debris), tugboat activity and power cruiser wakes.Best way to learn how tug operates on river is to follow one for a while.They make 5 or 6 knots and after doing so,you will instinctively know where you can safely anchor and still be out of thier way.Have other good references not handy at moment.If interested in more ,drop me a line. Good sailing. -Gary-