What rank would the league champions get if they joined the hero association?

Honestly,no one would be C-class,because C-class are essentially just regular civilians who are ready to help others and are either physically or mentally fit. Ashe with her ability to shoot ice-arrows(including a giant one) would easily qualify for B-class and the same would probably go for all champions.

If Taliyah is S-Class, I shudder to imagine ASol's rank.

Even in OPM, the rankings aren't exactly accurate. There's an entire chapter showing why it's not reliable.