I’d guess so - of course there are several Gospel passages that do as well (most notably ‘what you bind on earth will be bound in heaven’ and ‘who hears you hears me’).
But the rub is the Church has to intend to bind. Not all pronouncements are intended to be binding, or not in all places or on all people for all time. And because Peter is more specifically the rock, certainly any other pronouncement has to be in sync with what the Pope says, and not contradictory to it, to be binding. That’s why it’s more commonly expressed as Papal Infallibility rather than whole-church.