It does indeed! You can link your Strava account to Beeline when you set up your Beeline account. Then upload as many of your rides as you like.
If you are linking your Beeline account with Strava during set up, just follow the instructions on the screen.
If you have already set up your Beeline account and link your Strava account later on, just head to the Beeline app's settings menu.
Once your Strava is linked with your Beeline account, simply find the ride that you would like to upload, find the 'upload to Strava' button, and there you have it.
Your ride will be available to view on your Strava account as soon as it has been processed. Kudos!