Answered here: https://twitter.com/coinbase/status/892499250273107968

Will Coinbase keep BCC coins for itself?

No. 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.

Makes sense but if the value BCC is at sustains itself, it would make sense that customers see that value as considerable and lost if they can't reclaim it later on.

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.

You can bet I'll be removing every last coin I have from coinbase as soon as all of this is over. They gave a whopping three days notice. For those of us who had our coins in a vault, which adds a 48 hour delay to any transfers, this gave almost no time at all to react. In my case, I wasn't able to get it out in time and it essentially means I just lost money. Coinbase of course has no way to get a hold of anyone. I just have to watch my money swirl down a drain.

3 day notice? Did you check your emails from coinbase? I got an email on 7/19 warning about the fork.

The email laid out the process if you want access to the fork.

I got an email mid July