Will Coinbase keep BCC coins for itself?
Coinbase does not intend to support or interact with the new blockchain in any way. If this were to change, Coinbase would make those coins available for customers to withdraw, not keep them.
Ironically, not "interacting" with that chain only serves to create more dead coins and thus push up value. Imagine if the value grows considerably... customers might be changing their tune if they feel that they lost out and feel they were misinformed.