Could Claudio Reyna, free from the demands of the MLS season for the rest of the year, rehab on his own and rejoin the league?
Perhaps. It's not unprecedented. Alexi Lalas retired and always maintained that the rest it gave him helped him recover to the point where he felt able to return and play well for a couple of years. Jaime Moreno didn't retire, but he had a really crappy season with New York when he was traded there and many considered him washed up. He later revived upon his return to DC.
Three things would have to happen for Reyna to succeed in MLS, though, and I doubt they'd all fall into place.
1. The most obvious one would be that Reyna would have to get healthy again. That's no given, with his history. Chivas USA took a chance on John O'Brien in 2006 because of his relative youth, but his injury history was too extensive and O'Brien was a bust for the team.
2. Reyna couldn't play on turf. It's simply too much of a strain (charity games on the surface notwithstanding) for a player with his set of ailments. Reyna would be better off recognizing that and taking care of his body. Look at how Edson Buddle has thrived since leaving turf stadiums behind. Of course, that limits his options to teams that play home games on grass. So no Toronto, no New England and no Philly if they go through with their exploration of using an artificial surface. Of course, the Red Bulls are moving to a grass stadium next year, but I don't see this organization ever wanting to deal with Reyna again, or vice versa.
3. Reyna would have to take a massive pay cut. It's not unprecedented that a player with an impressive USMNT history would take a reduced salary in order to play with a specific team. That's exactly what Cobi Jones did in his final Galaxy years. Not only did this reduce pressure on the team's salary cap, but on Jones as well. Fans and management alike weren't desperate for Jones to produce, because he wasn't a massive financial drain. No one is going to pay Reyna a million dollar salary (no one should have paid it in the first place).
If these factors all fall into place, Reyna would still (unless the second rumored MLS team comes to fruition) be willing to leave what brought him to the States in the first place - the city of New York.
It's likely he's unwilling to do that, and done with MLS and his career. On the other hand, if his competitive fire is still burning, personal connections with certain organizations might propel him to return, perhaps to wreck havoc on New York. Longshot chance might go to Kansas City and Curt Onalfo.