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

Yes. However, this only works if the sender has inserted the keyword manually into the email body or has copied the email to the global address.

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.