Unless there's some roundabout way to do what you're asking, the answer is "no". As others have stated here, you can backup to OneDrive then download photos to a local directory on your computer. Go back to your One Drive and delete all your photos. Also, if you're an Office user, Office 365 offers a storage increase for active subscribers. I get 1 TB of storage for photos, which for mobile uploads will take a LONG time to filling up since there tends to be compression on uploads. The other option is to use an alternative like DropBox. Or you can just pay a few bucks and upgrade your storage for OneDrive. I know paying more isn't always a wanted path forward but using OneDrive for upload/backup is so easy and it's really a solid service - hasn't let me down in the 5 years I've been using it.
If you want a FREE upgrade on OneDrive, refer friends. I believe you can unlock 10GB of online storage if you get 10 friends to sign up. Just find friends that aren't already using it and help them setup a free account. Even if they don't want to use it going forward you still get the referral credit. If you have $2 a month you're okay parting ways with, you can get 50GB of OneDrive storage. I use 45GB of my 1TB storage and I've been backing up photos for years using only OneDrive. I'm not a camera fiend but I take photos and videos at decent quality and they look good online.
If I were you I'd opt for ease of use over the manual process of backing up to a drive and pay the $2/mo - though you can do both. When you max out your online space, move it all to your external drive and then proceed to try and fill up the next!