All else being equal, yes a narrower neck would be more prone to bend. But is the tension of a three stringer enough to do it? I don't know. Time to put on your lab coat and do some experimenting Bob... and let us know your results. : )
The thickness is way more important than the width. A good piece of hardwood with a nice straight grain should be fine. Also if you keep the shape closer to square it will be stiffer than a full "D" shape neck. I'd say go for it!
I agree with Kigar and I also use incorporate a extra heel piece to glue the through neck to so there's no way the neck can warp . My necks are made from Tassie oak 1" thick I have a endless supply of timber in my forest that I mill for different jobs .
I haven't done a through heel piece yet but it sure seems like a good idea.
I never thought about the shape, thanks. I've settled on a shorter 640 cm scale to make it easier to play 7th and minor chords rather than the ones I made at 25.5 inch. I just found some nice tight grain mahogany that is rough cut at plus one inch. I can probably get 18 necks from it. I'm very close in confidence to making some to sell to help pay for this fantastic hobby. I don't want to sell any that would warp.