With limited information available, Coinbase will not support Bitcoin Gold initially. Company promises to credit Bitcoin Gold if newly created blockchain is secure and proves to be valuable. here is statement provided by Coinbase:
The Bitcoin Gold fork is projected to take place on October 23rd. Information about this fork has been limited and there are concerns about its security and stability. As a result, we do not believe it is safe to allow support for Bitcoin Gold at this time. If the blockchain proves to be secure and valuable, Coinbase may choose to support it.
For more information about Bitcoin Gold please see our FAQ page.