No, nothing would have changed if that happened. Republicans have no qualms about overtly breaking the law and abandoning their duty and decorum. If they did then Garland would be a sitting SCJ and Gorsuch wouldn't.
If RBG had retired while Obama was still president, it would have been a Democrat appointment, no?
Am I missing something?
yes. Scalia died in Feb 2016 (while Obama was president) and the senate refused to hold confirmation hearings on a successor until Trump took office in 2021.