I think you're giving too much credit to the recruiting potential of a painted rock. The rock is cool and all, and recruits can get their picture with it, providing they go by, but I know for a fact the band has painted the rock every game day for at least the last decade. It's not like this is something new. If you want the rock painted for recruits, I suggest you do it AFTER the band paints it. Let it stay up for a while for them, then paint what you want.
Painting it at night with the expectation the band isn't going to paint over it is narrow-minded, at best. No one owns the rock, but I can assure you the band kids will paint it every game day.