Never heard of it being tried, but don't know enough about growth habit to say one way or another, but does it in fact get a woody trunk, have a reasonable lifespan and possibly bud back (on the lower trunk or rear-ward on branches) if cut? Does the trunk fatten up to any extent and then taper? Of course Cottonwood trees are used, but I've been around bonsai a looong time and no one to my knowledge has even ever raised the issue, though a lot of unusual things have been asked about (i.e. mesquite).

I'm not sure if cotton plants will survive for multiple years which would be a first important requirement. I live in Tennessee, and there is plenty of cotton around, but it's always harvested annually, and the remainders of the plants are left to die or plowed under. It is a pretty rough looking plant, so if you could get one to survive for years, it could work.

I live in Lubbock, Texas and it is covered in cotton. I know that they spray something on the plants before harvest that makes the plants drop all of it's leaves and open the boll. Then I think they just plow the plant under. No one seems to know if they will live for years if cared for. Not even botanical web sites. It's odd.

http://ipm.ncsu.edu/Production_Guides/Cotton/07Cotton-ch-02.pdf
go to that site and read. It is NOT an annual.

Here is a link that might be useful: Cotton info