No, I don't use coarse material in the bottom of my pots - doing so is not necessary, and could make things worse, not better. Autopots work by wicking of moisture/nute mix from the bottom of the pot, and a major change in particle size can impede wicking across the boundary.
In my recent grow, I used ~60/40 coco perlite throughout the 3 gal fabric pots, with no air dome, and I had dense healthy roots all the way to the bottom of the pot. See the review in my sig for more detail.
Bottom line for me is that keeping it simple works extremely well with Autopots, perhaps especially with fabric pots.
One additional suggestion though is, if you intend to use soil, it might make sense to put some 60/40 coco mix in the bottom of the pot to make sure that it aerates well with each flood cycle. Some soil mixes may not drain as well as 60/40 coco, and this could be made worse by using solid rather than fabric pots. Healthy roots in the bottom inch of the pots depend on that zone being aerated well during the latter part of the flood cycle when the nute level drains away, so you need to make sure that the medium down there drains well. The boundary between 60/40 coco and whatever soil you use should not present a problem for wicking.
Good luck with your decision, and your grow.