Not necessarily. If there is increased confidence in bitcoin by those who hold and mine them, such that they don't want to sell, the price will go up even with marginal inflow of fiat. We're all just collectively agreeing on price here, it could go to $10,000 tomorrow if there was (somehow) a consensus that that was the right price.
True, I was more thinking of the panic buying conditions recently experienced and the necessaries inflows required to keep inflating the price.