Are you a part of the RCIA team now? Your parish process sounds much like ours.
People in RCIA are already volunteering in parish projects! (And not just little ones!)
I’m not an RCIA minister, however I am part of the ministry at my parish. Right now, I’m helping in the adolescent faith-sharing ministry which, of course, is part of our overall faith-sharing program. We meet after regular mass every Sunday.
I would definitely be available as a counselor or sponsor in future RCIA planning.