Does anyone think thumbprint cookies will work if I use fresh cherries for filling?

As davidpdx suggests, before filling the cookies, I would cook down the cherries with a bit of sugar until they take on a jam consistency. If you want to leave the cherries more in tact, a pie or clafouti might be a better route.

I think it not likely to work well. Fresh fruit will have too much liquid that will exude during baking, making the cookie soggy and fall apart. That said, there is never any harm in just playing around with a few test samples--make some with fresh cherries; some with cherries boiled down with sugar. If they do not work, you can always use the extra dough for other cookies.

Have you thought about making a terrific cherry clafouti? (The old Julia Child recipe works well.)