Question about syncing Outlook (Office365) mail with Gmail

Hello, thanks for checking out this post!

Had a quick question re: Outlook's https://imgur.com/a/4eOv6e9 capabilities. We're about to end our outlook accounts, and are curious if we sync with a Gmail account before doing so, will all the old mail remain in the Gmail account even after the Outlook accounts are deleted? Would appreciate if someone could spell out exactly how that works. 

Many thanks!