I would not do that. For the paint to stay and not peel off, it would have to never harden. I would simply contact the manufacture and inquire about the cost/trouble to replace the screen material. If you are thinking about screen goo, it is for a wall.
You obviously don't know what your talking about regarding the application listed, and propbably about the subject as a whole.
I personally have sprayed several screens with NEVER an issue after lengthy periods of time "after drying" and literally hundreds of Roll Up-Roll Down cycles.
The screen in the link was demo-cycled repeatedly at least 10-12 times daily for 21 days straight,,,,and has stood the test of time since then (November 2012) I painted a 135" Elite Electric in 2007 in Rancho Santa Fe, CA and it's still wow'in them.
I can understand how the uninformed can question...even discount the possibility, but until they understand the make-up of the paint, and the application method, they can't grasp the potential....let alone the reality of it all.
Still, one who is not familiar or experienced with such things should not express such definitive opinions.