Only if the non-Catholic was baptized and married to another baptized person.
Good point. Here's two scenarios:
Non baptized person (divorced) wants to marry a Catholic. a) annulment still required? b) baptism required, if married in The Church?
scenario #2:
Baptized person, divorced from non-baptized person, wants to marry Catholic. Annulment still required? Or does the Church still recognize this marriage?
(no wonder this was hard work, Sink! It can get tricky, lol)
Two baptized persons are presumed to be in a valid marriage.
You may be thinking of the Petrine privilege, where a baptized non-Catholic is married to an unbaptized person and wishes to marry a Catholic. The Pope may dissolve the marriage in favor of the faith, to allow the baptized non-Catholic person to marry the Catholic.
There is also the Pauline privilege, where two unbaptized persons marry, then one decides to be baptized a Catholic. The Catholic decides to dissolve the marriage. The Pope can also dissolve this natural marriage, after a civil divorce.
Both of these cases involve non-sacramental marriages, so the Pope is simply dissolving a natural marriage. These are not annulments, but the tribunals do the paperwork to forward to Rome.