"Is it possible to have the Takedown program on multiple devices for the same team?"
The key to successfully using Takedown’s data sharing facility is to designate one iPad as the “official” source and share your season from that iPad out to your satellite scorers. When the event is complete, have them share their season back to you for consolidation. The import process is additive — the imported season’s data is added to an existing season of the same name. Also, your satellite scorers should only score matches and add opponents. You’d repeat this process for every event for which you had multiple iPads scoring.
All along the way, you should be backing up your “official” Takedown instance so you’re covered if you ever need to revert to a prior instance of your database. Backing up your data is simply sharing your Season to a safe place, your inbox, Apple’s Notes app, Google Drive, Dropbox….any place where you can safely keep a file.