Not much via ferrata on the AV2, but assuming good snow cover; multiple terrain traps and slopes of differing aspects and elevations each day.....avalanche poodle territory.
You would need very good settled weather and consolidated snow on all aspects and heights to safely complete it. Not being a Dolomiti local I don't know how rare such conditions are, but suspect they are unusual. It would be an impressive trip...
Note the winter ski-touring lines diverge from the Alt Via 2 route for good reasons.
If its a dry January with little snow it certainly would be possible.
Post edited at 15:34