If the leak is from the axle seals, it's probably too late and you're looking at replacing all the seals - which would mean you could continue using synthetic. If the leak is at the plug, maybe there's no problem (until there is, in which case it's too late and you're looking at new seals).
So if the seals aren't leaking yet a flush is a good idea. If it was me I wouldn't assume ATF has no synthetic additives or other odd stuff. I'd use a light weight non-synthetic motor oil and jack up the rear wheels while you spin it up to splash the oil around. (Motor oil doesn't have the high pressure additives a loaded transmission needs.)
Motor oil is built from the same stuff as hypoid lube, so you know they'll mix well and give a good flush. ATF has a lot going on in there, and it's anyone's guess how it'll mix with gear lube.
Chris