Of course this will increase the price, when eth 2.0 goes on the gas fee will be much cheaper than now
That's the purpose of the 2.0 and EIP 1559. They're about to lessen the fees which has been painful for most of the people that are transacting through ETH.
The increase in transaction through NFT has also contributed to the increase of it just like the cryptokitties days.
We can't further tell how effective will be this ETH2.0 upgrade until the moment launched. We are just hoping that it gives a huge help to lessen the huge fees that we cried about. We still have 4 months to wait and I don't think that people can still wait that long and able to hold their ERC20 tokens and never be driven by their emotions after seeing some declines.