ETF bitcoin will be equivalent to paper bitcoin (a centralised ledger outside the bitcoin ecosystem and thus its blockchain). The assumption is that the ETF providers must hold an equivalent amount of bitcoin in order to supply the ETF (One paper bitcoin promised IOU equals one real bitcoin in holding).

What gold ETF teaches us is that this does not need to be the case. There is way more promised paper gold than gold around.

The only way it could impact the price is if the trust in full reserve of gold or bitcoin holdings is questioned. The questioning will occur if the majority of people having an ETF would like to see it converted in real gold or bitcoin because fhey want to self custody based on lack of trust in the centralised IOU system.

This could create insane scarcity if too much fractional reserve was allowed in the first place. Say; an ETF IOU bankrun would occur...