That depends. If you mean people who played in the actual NFL then playing gridiron for fun, with pads, then no. By the time they're done their bodies are usually shot. If they left early enough, it's possible but unlikely, because they've already played at the most brutal level and it's not exactly something they do to relax.
If you mean people in general playing gridiron for fun as adults, yeah, that does happen. There are amateur and semi-pro leagues that play with full pads. A friend of mine played on a semi-pro gridiron team in Texas for fun when he was stationed there with the army. He had to buy his own pads, and many of the players were former high school and college stand-outs who just didn't make it through college and into the NFL. Some of them go on to play arena football or in a developmental league.
But if you count flag football and touch, then lots and lots of people play into adulthood. Many cities have adult-age flag football leagues through community centers and universities, where anyone from the public can play. Cops and fireman also play in flag football leagues against each other. It's not uncommon. And it's kind of a tradition for people of all ages to just play backyard games of football on holidays -- especially in the snow on Thanksgiving. The only real difference is the lack of pads, tackling, and defending the line of scrimmage is just a lot of pushing instead of big wholloping smacks.
But as far as team sports go, I'd say far more people in the U.S. play soccer and basketball into adulthood. I'm not counting softball, because any game where you keep a keg of beer at second base skews way more to the recreation than the athletic side of the spectrum.