I’m thinking acrylic paint shouldn’t but if you can find some old ripstop nylon (which is what I’m guessing it’s made out of) you can test it and see what happens.
Watch out for solvents. That’s what’ll eat the nylon if anything does. Spray paints tend to have some pretty aggressive solvents in them.
Now that I think of it, I’d be better off buying some of that camo netting and throwing it over the tent. Maybe even two layers of it to be on the safe side.