Not really the way you asked. I don't know how much customization outlook allows, but basically your only option is to send an email and add the ticket number to the title. Then your inbound actions need to be able to recognize that (even if email is marked as new) and connect it to the record.
So, if user sens an email with subject RITM1938958 - Question, the inbound action can look for a RITM number in the subject and use that to connect it to an existing record
I believe SN should already have internal logic that is able to see if reply is related to an existing record, but when sending a new email that doesn't seem to work. There's a property that handles recognizing emails as reply depending on a prefix on the subject (re:, RE:, Re: usually ), but you can just as well do that with an inbound action. But of course the user needs to know the number and I don't know any way to integrate outlook to servicenow in a way that would give a list of existing records.
