Yes, but because of the limitations of the Bitcoin blockchain, the exchanges can find efficiencies by putting the BTC on ice and creating a faster, internal coin for transactions. You only really need to think about the uniqueness of each Bitcoin when you are settling someone up. When a customer asks for their $$ back, you better be able to give it back.
I believe we've seen this in a couple of places over the last few months.... certain coins had wallet maintenance at very pivotal moments. You can bet that the exchanges have a certain amount of fractional lending going on. If they have to get called on it, this seems like one killer way to do it. They may have customers with claims to someone else's Bitcoin-Cash. And when those customers find out, they will vote with their feet.