I think I see where you're going with this...
If the 2x2's are also glued and screwed to the concrete wall. I'd use something like Tapcons.
Buildex Tapcon®
You can get them cheaper at Home depot, they come in a kit with the bit.
Go right through the 2x2 and into the concrete.
If they aren't attached. You mentioned the mount spans 3 studs.
I'm willing to bet three 2x2's will hold the TV without a problem.
If the mount is one of those articulating are types, and the 2x2 aren't attached to the concrete....
You're going to be better off cutting out a section of dry wall and adding a few wooden braces.