Yes, you can. A team simply cannot sign every player it drafts. First, there's a salary cap. And second, if you signed every player you previously drafted, it would negate the purpose of the draft itself.
Well run teams, Pitt, NE, Green Bay, have a carousel of players. They don't overpay just because they drafted a player. That's not smart. Now, they also don't overpay for other teams' picks, but draft smartly. If you draft right, you don't need to overpay for your players.
As for Byrd, tag him again. Aaron Williams can pick him up at the airport. Welcome back, Byrdman.