Probably yes, because a large part of the float is held by people or firms with exposure other markets, so there would be selling, gotta get liquidity to cover your arse

As cash appreciates, everything gets repriced again, not cash still debases over the long term so why would the value prop around Bitcoin change?

I don't think we get a deep and prolonged recession, bad for business and social cohesion, people will not take the pain well, not when there's a band-aid called money printing to swoop in and paper over it all.