The idea is feasible but probably under certain conditions such as cold weather, high oleo pressure, starting refuel from very light load causing a heavy drop, but can't say the aircraft settling during refueling has ever caused me a problem when aligning the ADIRUs. I think you'd have a problem specifically saying it was the refueling causing a problem when pax and freight loading could also be going on also. Sudden settling is more noticeable on the A330/340, and they have never caused me a problem either. If the ADIRUs do not like the excess movement, you get an ECAM message and just do a re-align, so does not cause much of a problem anyway, which I have seen if towing the aircraft during an alignment which could be an excess airframe movement or change of GPS location if using GPS align.
Generally, most of the time I'll have the ADIRUs on for refuel (pitch and roll inputs to FCMCs required), and it is the crew who do the alignment and I've never seen a crew hold off until refuel is complete either.
Having said all that, I'd also need to check the AMM ADIRU alignment procedure for any warnings and cautions which would override my experience.