@elise1 yep that should work just fine. We have a number of customers who are doing something similar. As long as those contact owners have their inboxes connected to HubSpot (personal or otherwise) we should be able to generate the data that shows up in the email reports.
If you want the email to be logged to the contact timeline though, then you will need your reps to have their inboxes set up as team inboxes. Instructions here for that.
Hope that helps.