Actually, while I doubt it would work, I wouldn't say it's impossible. CDs have error correction on them. That's why you're supposed to clean them wiping from the center out, rather than around...scratches that go with the "grain" of the data are less likely to be fixed by error correction than spoke like scratches that cut across tracks. Depending on the break it might even be possible to get the cracks to line up.

That said, I wouldn't try it, I'd doubt it would work and there is a small chance you could damage the drive. I'd just get a new copy.