... if my party rep is 20? I'm thinking of picking them up to do their respective quests.

If 20 is too high, what is the max my rep can be before they will join? 18?

I think that they'll join no matter what your rep is. Your rep won't bother them UNLESS it changes is the way that I understand it. So, they'll be fine as long as it stays at twenty. However, if it goes down to 19, good bye Korgan & Edwin.