In baseball, is it possible to definitely break a bat with a pitch?

Only on a wooden bat.

Sure. Happens fairly often. Wooden bats only, of course. Happened to me when I was fourteen playing ball. Flipping thing splintered from a fast ball and vibrates up my whole arm. Hurt like hell.

Yes, frequently.

12 years old in Little League, I broke.

https://www.youtube.com/watch?v=51V7VBk3r8I

I will add that Jose Canseco and Mark Maguire (aka The Bash Brothers) used the sand down the handles of their bats, and they broke a lot of bats, and a few home run records.

And they both used PED which had something to do with it.