Will I get Obyte Cash if I keep my Obyte in the exchange?
That's up to the exchange. Better not risk it. Obyte has a very easy to use light wallet. Just withdraw everything there the day before.
We do not have any control over what the exchange does and so we would strongly recommend to keep all your GBytes in your own wallet (the wallet whose private keys you control) at the snapshot time. This will guarantee that you receive the airdrop.