The NFL undoubtedly pressured teams, especially those with the last 10 picks in the 7th round. I’d be willing to bet if the Rams didn’t draft him, the Cowboys would have. In reality, Sam would have done better being undrafted- he could have picked anywhere to sign, a team that he’d have a shot to make. The Rams d-line has so much depth, it’s highly unlikely he’ll make the team.
No, he can’t pick where he would sign. A team would have to offer him a UDFA (Undrafted Free Agent) contract.