Take it from me ...I just replaced the drywall in my livingroom, prime
it. An unprimed sheet of drywall will do nothing other than suck up
any moisture put on it. You will have a h*ll of a time removing the
texture in say 10 years if you don't. And I don't know how well the
pain over the texture would turn out if you don't. I havent ever
texturised anything but I'm going to venture a guess that the paint
color will not look as nice if the texure isn't in good shape (too
thin in some spots bc of no primer).

Tammy