Honestly, it is a distinct possibility. Check the laws in your state to see at what point you have to modify child support based on custody.
For example, in my state, the cut off is 90 days a year. If my ex has the children more than 90 days a year, then he could petition to adjust child support. Because he only has the kids something like 70 days a year (e/o weekend/Spring Break/1 week Christmas/ extra time over summer) then he pays me full support.
I have a friend here whose WS tried to slip past that law by arranging to have their children something like 95 days a year...fortunately her L caught it. She keeps his visitation under 90 days a year.
If it were me, I'd keep a copy of that classified ad, and anything else suspicious