On the contrary, it makes a significant difference. Futures have to roll over monthly and there's costs associated with that. Depending on the slope of the futures curve, the costs can be high (10+%). Holding spot bitcoin solves this problem and makes the fund more palatable to advisors and institutions.

Your original question was about price. Institutional demand in an asset generally reduces its open supply. That should affect the price.

If someone buying into the bitcoin ETF takes away the same transaction from Coinbase then the net result is the same.