Thats all we do at work when we do a differential service. Unfortunately quick lube shops don't have the time to take covers off and re-install them, it just wouldn't be worth it. We use a pump to suck all of the old fluid out on diffs that don't have drain plugs. We do pump new fluid in and suck it out so it gets somewhat of a flush.
1977 J-20 TeamRushed AMC 401, TH400, D44 front, D60 rear, 33x12.50R16.5 Mud Terrains, SOA, rear shackle flip.