I'm not chemist enough to know whether the coatings you mention would cause a high TAN, but the assembly and break-in contaminants alone warrant a change of oil. 500 miles is the minimum time but I would gauge that by the shop and the reason it originally failed. If the axle failed catastrophically, there will be a lot of metal in the housing and spraying it out with brake cleaner (a typical method at an average shop) isn't likely to get it all. If the shop pulled the housing and hot-tanked it, or pressure washed it out, maybe, but my experience is that break in is still occurring well after 500 miles, as evidenced by the magnetic devices I've observed. No studies I know of, but the new diff in my own truck quit "fuzzing" the magnet after about 10K (one diff change done earlier)
I spent time at an axle-only repair shop that had a big pressure washing tank into which you could put whole axle housings. Hot water, chemicals, hours of cleaning and still sometimes you could find metal paste gooped into corners. Lots of stuff gets tossed up into the axle tubes as well. If you turn a broomstick into a giant "bore brush" you would be amazed and revolted by what comes out of an axle tube after many years in operation and a major parts failure.
Based on my own observation alone, no scientific studies, if the unit failed catastrophically, and it didn't get a super-duper housing cleaning, I would change it at 500 and again at 2500-5000 miles.
