Don't see the reason why would they do that, this is just another altcoin, doesn't have anything to do with Bitcoin. Anyway, I got the feeling that majority of exchangers, at least those bigest and most important ones, will not support BCC. Could be a lot of confunsions before and shortly after August 1 until everything gets back to normal.
The reality is that bitcoin cash is getting more support from the community and it is a really good news for the traders in bittrex as they do not need to move their coins to their wallet and instead they could continue trading as usual ,i see that some of the markets are not accepting it but in this situation they could loose some profits because everyone will withdraw the coins at this period and i think supporting them will not harm their profits.