Pokemon Go - PVP Status after massive Power Up

So, If I have a pokemon that has 97% good status for PVP, and I go over 2500 CP, does it loses its good stats for PVP?

I'm asking that because I have a good pokemon, with 90 IV and 97% stats for PVP, and I'd like to use it against Giovanni.

But I need to power it up, and I wonder if keeping it at 2490 is gonna do any good agains Giovanni's Persian that has a CP over 7k or so.

Its 97% stat is for a specific league, in your case it seems the 2500CP or Ultra League. Powering it above 2500CP makes it ineligible for that league. If you want to keep using it in PvP, do not power it up!

In more general, the best IV changes per cup per Pokemon. Take for example Swampert, a Pokemon that is doing very well in each League, has a perfect PvP IV of 0/14/14 in the Great League, a perfect PvP IV of 0/14/13 in the Ultra League, and in the Master League obviously 15/15/15. So the 97% for PvP changes from league to league.