Does Deskhero import my old emails when I connect a mailbox?

Yes, for Google and Microsoft mailboxes an initial import runs automatically. Deskhero imports recent emails from your sent folder (currently up to 250) as AI knowledge, and if your workspace has fewer than 10 existing tickets it also imports a small batch of recent emails (currently up to 25) as tickets so you have something to work with. The connect screen describes this: "By using Microsoft or Google we will be able to synchronise your emails and auto-import your latest emails as tickets."