If we’re going by previous key VNs (Clannad, LB, rewrite) they all had their main menu graphic change once you reach certain point(s), so it’s not unreasonable to expect something like that I think.
That said, I don’t really think said change would be an additional character on the right, since that would kinda disturb the thing Ao has going on there… I’m more hedging with the main menu text just being on there as Takafumi said, and the change would be something else.