No, some methods of counting rank choice ballots will sometimes pick a candidate who was no one's first choice. In particular, this must be so for any Condorcet method, because the Condorcet winner might be no one's first choice (imagine a setting where 1/3 of voters want candidate A then D, 1/3 want B then D, and 1/3 want C then D; 2/3 of voters would vote for D whether run head-to-head against A, B, or C, and yet D got no first place votes).

In instant runoff it is certainly true that the winner is always someone's first choice, and that was my point - sometimes the winner the method selects should not be the winner.