If I have BTC on exchanges such as Kraken and Bittrex on 10/25, will I still receive bitcoin gold on 11/1?
That depends on the policy of the exchange, Bittrex for example credited their users with BitcoinCash shortly after the fork.
I am not sure what their stance on the current fork is, so you should figure that out.
It is always better to get a desktop wallet, to make absolutely sure you get the coins from the fork..