This will pump bitcoin cash,it won`t dump it.If such a major player like Coinbase shows support to bitcoin cash,this builds more trust,which means that more people will buy BCH.
This might create some speculation bubble for BCH,and when the bubble bursts,some people might return to
the real bitcoin.
It will definitely cause a dump. Coinbase will release BCH not because they support it but because it's their duty as custodian, and they will just let people move their BCH from the exchange if they have any due to hodling coins during the fork - it's not the same as listing it. BCH survived still because most people didn't want to bother dealing with its software to get some additional 6% of their Bitcoin value - Bitcoin itself is growing by dozens of percents per month. But if Coinbase will release BCH coins, it will increase the actual supply of BCH since there won't be any need to go through the process of claiming it, so it will crash the price unless Jihan Wu and Roger Ver will decide to pump their stillborn creation again.
As for BTC, it simply doesn't care about altcoins, because Bitcoin is the king of crypto.