No, it absolutely hinges on how you define fascism. Lots of people are calling conservativism and even libertarianism fascism and that is just not accurate, and it hurts more than it helps. If that were the case then humanity has lived under fascism its entire history.

Wealthy people are just people, so there are wealthy Marxists and Anarchists just like there are wealthy Fascists, Monarchists and other designations. If there’s any movement that is a wealthy people movement it is neoliberalism or neoconservatives (same thing different color), which has failed horrendously. And despite its failures they keep pushing it, because it’s the only system that can sustain their wealth long term.