I know for sure that CZ does, because I have seen one at the range. I didn't shoot it, but I saw it. The owner had handloads (don't know the specifics), but it did have plastic tip bullets. He said that he loaded his ammo to .280 Rem performance. The only thing that I can confirm is that his gun and load were quite accurate, getting what appeared to be 1MOA or better (his target was 2 tables next to mine). Of course this doesn't mean that all CZs in 7x57 will shoot the same.
Personally, I like the 7mm-08 over the 7x57 for two reasons: 1) the 7mm-08 is a shorter cartridge, and 2) the 7mm-08 has a far larger selection of factory ammo available. The benefit(s) of the 7x57 is that: 1) it has a "history," and 2) if you handload, your handloads can be loaded to higher velocities than the 7mm-08 and, from what I understand, be loaded close to .280 velocities.
Zachary