Can a user send an email to a contact from Outlook, outside of the Digital Sales UI and still find it in the activity feed?

Yes, but only if the sender has inserted the keyword manually into the email body or has copied the email to the global address, they can find the email in the activity feed of Contacts in Digital Sales.

All the subsequent emails and replies are also saved to the activity feed.

Note that if a sender copied to the global address only or the recipient removed the original message that contains the keyword, the replies won't be captured.