No, it will not, there is no reason that this project can affect ETH price in the future considering its popularity right now.
it might affect ETH price in the future if this project has more supporter or an advanced technology compared to ETH right now. But currently, it does not have both of it.
more importantly, this project chooses to fork ETH itself as their code source.
REMEMBER, they are forking the source!
Until we see the finished product developers, we can not judge its prospects. Bitcoin and Ethereum also started as a small startup.