Nope it sure doesn’t! All teams reset with the release of a new TSB. However, you will be able to select a few players to take over with you into the newer tsb.
During an event a random team will be given an extra boost! For example: this weekends team is the Orioles so all Oriole batters get 5000 per rbi and pitchers get 5000 per k in points. Hoped this helped!