If mild rheumatic fever is untreated & runs its course without serious complications, is an untreated strep infection likely to cause a relapse?

Possible. Doesn't really matter if rf was initially 'mild', although i'm not sure what that means. Recurrence after another strep infection is always possible, but not definite. Yet the drawbacks of having repeated rf episodes are not good, particularly for the heart. Antibiotics are likely recommended chronically.