About Logs Kept on Host, and VirtualBox's FDE


Using Whonix with Virtualbox on an Ubuntu host that has FDE. I was wondering however in the event that an adversary managed to gain access to the host OS when it was powered on, are there any logs that are kept which could de-anonymize Whonix usage/sites visited etc? I don’t know how the browser works in Whonix is it just that it keeps history but deletes them (so technically the history could be recovered forensically) or it doesn’t log history in the first place?

Would using VirtualBox’s encryption on both the Gateway and Workstation solve this issue - And would using that encrypt any sensitive data on both of the Whonix OS’s that were there BEFORE I encrypted them?