Anecdote votes against it.
I was on a deer hunt in N Tx near the Red River when my host saw a flock of turkeys as we were driving across the ranch and bailed out of the truck with a 10-22. I took a short-barreled Mossburg 12ga loaded with 3" magnum BB loads, and we pursued on foot through the creek bottom. Finally found the flock again in a clearing in the trees, and I started to whisper to my host that we should pick a tom each and stalk up a little closer, when he dropped to one knee and began popping away at one... at 60-plus yards! He rolled it and began to shoot another bird. At the distance I was at, an open-choke shotgun just wasn't feasible. The entire flock, including the bird my host had knocked over, flew up and out of the creekbed, never to be seen again. I don't know how many hits my host made with the .22, but he hit one at least one time, with poor results. I've twice seen that man make 320 yard shots on deer, so I suspect that the hits were solid COM.
Now, would I support the use of .22LR on turkey? Depends. If the shot could be made from a better rest, from 40 yards or less, in less of a hurry? I suppose. But I'd at least want a .22 WMRF, and would prefer a .22 Hornet. Also, learn your turkey anatomy-- it's harder than you might think to know where the kill zone is on a big tom's body. Learn to limit yourself and pass up the chancy shot, when using marginal rounds.