Where there has been a profound conversion, there usually is a worthwhile testimony -- and testimony is more or less a fixture in Congregational worship. I generally have two "rules of thumb" in this regard:
• Let the person share it first in a Church group, then with the Church, andOne may argue that a person should make immediate public confession and be baptised. In my experience, there have been too many people who did that, but did not prove themselves shortly thereafter -- for example, going on another drugs binge. In city ministry, one even has people who fake conversion if they believe they will derive some material benefit from it. OBSERVATION: My Churches have generally planned public testimonies, rather than putting people up impromptu. I think this guarantees the quality of a testimony, in fact broadens the "pool" of testimonies, where the impromptu approach might favour a certain kind of person.
• Look first for some abiding fruit of conversion.