There was a recent post with sort of same question..the short answer is ..no. Maybe you could coat the cotton .... Personally I don't know with what...but it would not be sublimation. True Sublimation process actually dyes the fabric...which is why it is only used in white or light pastel garment. What you describe would be nothing more than a transfer ontop of material.
If you want to do cotton you might want to check out Chromoblast....like sublimation inks, it is pricey, but works