Is Bitcoin Classic binary-compatible with Bitcoin Core? I have three full-nodes running Core 0.12.0 that I'm considering moving over to Classic.

Am I right in thinking that Classic is binary-compatible with an existing blockchain download?

Would I be able to just uninstall bitcoind from the Core PPA and install it again using the Classic PPA?
Since Bitcoin Classic is a fork of Bitcoin Core, this should indeed be possible. The problem though is that, should Bitcoin Classic switch to larger blocks and Bitcoin Core stick with small blocks then it will not be possible to switch back without Bitcoin Core downloading the whole chain again. But in that case we are quite in trouble anyway :-)