Yeah, it would be a pain to code, but not insurmountable, I guess.

I agree that it's likely possible, but I doubt an exchange would want to do a lot of custom coding support for Steem, especially since there isn't easy API support for it.

Coinbase does it with Ethereum and other tokens.

I'm not sure how other chains do things, but I suspect their staking rewards are tied to particular transactions on the chains rather than the vests/SP thing that Steem does, so they look more like discrete transfers that can be credited to individual accounts on the exchange.

Not sure if it would impact curation rewards.

I think it would only do that if the exchange accounts voted, the rewards distribution is based on actual votes recorded on posts, not possible voting power.