Here is May's Schedule:
Carowinds May Schedule
Notice that they are only open Fri-Sun, with a couple Thursdays in the middle and of course Memorial Day (when daily operation starts).
Memorial Day would obviously be the busiest day the whole month so I wouldn't suggest that.
The Thursday & Fridays there will likely be education days which will have many school groups, but won't be as busy as when school is out for summer. You should be fine without a fast pass these days. Fridays generally will get busier in the afternoon as schools lets out however.
Of course if it ends up busier than you're comfortable with as far as wait times, you can always get a past pass at the park. I wouldn't prepay for it. Just wait and see so you don't end up wasting $. I went in June last year while school was still in session and saw many people with fast pass and no lines were longer than 10-15 minutes (except Nighthawk was 30). I would have felt cheated, but to each their own if they want to waste it...lol