"Bitcoin Cash is the real Bitcoin" seems to be the value proposition of Bitcoin Cash. If Bitcoin Cash ever should get more valuable than Bitcoin (and hence get more miner support and hence become the longest chain measured by proof-of-work), then I believe it will replace Bitcoin. On the branding, there won't be any "Bitcoin" for a while, only "Bitcoin Core" and "Bitcoin Cash".

The way Bitcoin Cash can succeed is by replacing Bitcoin as the "lingua franca" of cryptos. Today it's super-easy to convert Bitcoin to/from fiat, and anyone accepting crypto will also accept Bitcoin. If Bitcoin Cash gets sufficient amounts of merchant support and gets as much coverage as btc in trading pairs on the major exchanges, then demand will grow - if people can choose between paying a significant transaction fee and paying an insignificant transaction fee, then why not choose the latter. Demand for Bitcoin Cash could grow a lot, while the demand for Bitcoin is going the opposite way.

Is it likely to happen? I don't know.