A punt returner (or kick returner) needs to have two skills: ability to catch the ball, and ability to run forward while avoiding tacklers. He doesn't have to learn about blocking or protection schemes or any of that. This guy really doesn't have to learn anything about American football to make the team at that position.
If he's going to play on kick coverage teams, he does need to learn a small number of things: rules on tackling, and the responsibilities and coverage of his cover team. Not very much. I'd be surprised if someone couldn't _learn_ those things in a couple of weeks. Of course, some players _learn_ the cover scheme, but nonetheless don't cover their lanes properly, so there's no guarantee that he'd be able to carry out his job properly.
So, I'd guess that a guy like this could join a random team and contribute as kick returner within a week or two, assuming that the team's existing return guys are all bad. Would that be worth a roster spot? Probably not. He might be able to play coverage within 5-6 weeks. Would the combination of return-man plus cover-man be worth a roster spot? If he's good enough, sure.
The Patriots have a good punt returner. They don't have a good kick returner, but that position is less important, since most kicks can't be returned. I don't see him as a useful piece in the near future for New England, but I could imagine him playing for some other team which has mediocre/bad punt returners.