Another year I had the exact same situation (backup's iOS version newer than the newly delivered phone's iOS version), and iTunes actually refused to restore the phone from the backup until I updated the phone. I'm not sure what is different this year, but iTunes dove right into the restore before I even noticed that the phone was on 10.0. And then it asked me if I wanted to upgrade the iOS WHILE my phone was still syncing Apps/Music. I told it to wait until that was done, and then I started the update manually.
Good to know! Maybe I'll just try it your way. Seems easier