Lowest mileage, yes.
I would, at an absolute minimum:
When you pick it up from the junkyard, grab the driveshaft flange and twist it. There should be very little play rotationally and zero play up/down and in/out. If so, give it back to them.
Drain out the fluid that is in the assembly, god knows if water got in there. Pay very close attention to what that old diff oil can tell you. If it has a slight gold or silver sheen to the oil, it is an indication that there is a bearing in the axle assembly that is failing. If you see that, put it back together and return it to the junkyard and tell them why you are returning it. Pretty damn sure they would have no issue taking it back and giving you another once you describe what you saw. Also, once you have it drained, swipe around inside the fluid that does not drain and feel for any grit or metal particles, if you find any, save the piece and bring the assembly back. Show the Junkyard what you found.
Take the axle shafts out and look at where the axle bearing rides. Shiny part in the pic below:
If you can feel any imperfections with your fingernail, take your "old" one apart and check your existing one. If both are "pooched" get an "axle saver" bearing set and replace the axle bearing with that. It is an integrated seal/bearing that rides in a different area of the axle. Either way, install the better of the two axles.
If your axle shaft checks out OK, check the axle bearings that are pressed into the axle housing. The bearings in the cage should be shiny with no imperfections, also very little side-to-side movement. If the bearing fails any of those checks, replace the axle bearing.
(check this thread:
Replacing axle bearings)
Axle seals are a must, replace both sides. On the inside of the seal, there is a little groove with a spring in it. To keep that spring in there when driving the seal into place, fill the groove with petroleum jelly (vaseline). It won't hurt anything.
New, pretty one in the pic:
ALWAYS, every single time that you remove the cross-pin keeper bolt, get a new one. Do not re-use it, ever. They do break, and are not very fun to get out after it does. It is circled in red below:
Next would be to give those spider gears a look. If they have alot of slop, replace them too.
Once this is all done, I cleaned out the gray goop that sticks on the inside of the assembly with brake cleaner, elbow grease and plenty of rags. Once it is all cleaned that way, put it back together and add the oil. Make sure everything gets a good coating of oil too since the brake cleaner will remove all of it.