Japan's helicopter destroyers become aircraft carriers in practice

Are Japanese helicopter destroyers really carriers if they receive ski jumps and F-35Bs?

Yes; once equipped to operate fixed-wing F-35Bs, they function as aircraft carriers regardless of the official label.

Ships modified with ski jumps to operate F-35B aircraft are carriers in practical terms. The official helicopter-destroyer title does not change the vessel's aviation function. Political or institutional labels can therefore diverge from naval capability. The later discussion of cruiser and destroyer terminology develops the same classification problem.