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.
One of the greatest advantages of Bitcoin is that it is a non-correlated asset. This means that price movements are not related to an underlying share or currency value. I believe that all investment portfolios should contain non-correlated assets to preserve wealth in times of economic uncertainty.
While I completely agree with you, it still doesn't automatically mean that bitcoin is going to perform well in a recession though.