Mathematically yes, there's nothing preventing ETC from doing the same thing. But ideologically, the lines have been drawn. At least for the time being, I think it's a safe bet that people who aren't committed to decentralization will just go with ETH instead of investing in ETC and voting for future forks.

Again though, I think the design of both cryptocurrencies is prohibitively error-prone, so it's kind of a moot point.

No, ETC will still be ETC, new forks will just get new monikers. I'm holding out for ET-TNG.