Based on my understanding with BTG, there is a chance if you send coins after the fork to a new wallet address, it could unintentionally send BTG along with BTC. If you control both wallets (the address sending funds from, and sending funds to) you should be able to access BTG no matter what. How that comes into play when sending to an exchange is another story, as you do not technically own your private keys. If you want to play it safe, wait until resources come out to split BTG and BTC prior to moving funds.
That would be a major hassle and not worth the risk if you're a trader since it seems that BTG developments have completely stalled and we haven't heard much from their dev team. There only exist a single way to claim BTG, and I think that alone isn't worth it as of now. The fork was a complete mayhem all in all.
