Psavola's comment is a little misleading, since the 5-20% roll is independent of score. What more score gives you is more countries rolling for that increase. But they could all roll under 8% if the dice are against you.
The really important thing is not the cumulative score, but rather how much of the score is X-Com vs aliens' negative score. If your 10K score is made up of 15K X-Com and -5K alien, that's a lot different from 10K with 10.5K X-Com and -0.5K alien.
Countries have local X-Com/alien activity, which can significantly influence the chance of getting a funding increase. If your mod has a gazillion countries, like XCF, that's less of a concern, since most of them won't see much activity. But something like vanilla with 20-ish countries is a different matter.