Most probably some could use Bitcoin as a safe haven to hold (or hide!) money, but at the end I expect the bigger investors withdraw and use that fiat to buy falling businesses. It may make more sense economically. It depends though how volatile will Bitcoin price still be near the start of recession.
It's actually not the big investors who I expect to dump their coins, I personally think it's mostly those who didn't know what they put their money into. It's safe to assume that there's still a lot of people that think bitcoin is just a get-rich-quick scheme.
You are right. Just I expect that the (sum of) money of all those try-to-get-rich-quick is no match for the really big whales, the ones that have bitcoins enough to buy entire businesses.
Also the small fishes don't affect the price, since they don't buy or sell all at once, while we've seen the whales doing that.