To the question at hand, I thought the building was formerly a Verizon warehouse. Harvard bought it and the first project that was to be built at Barry's Corners was an art museum gallery / conservation (storage) building. There was objection from the neighborhood, one objection being that the proposed building wasn't grand enough, wouldn't be a sufficient magnet to draw people to Barry's Corner. So Harvard shelved it, and decided to rebuild / expand the Fogg instead.
I would very much doubt that the Fogg's artworks would ever be stored in the former garage.
I believe Harvard is converting the garage to now house a ceramics studio and other community-oriented uses that are currently in buildings to be demolished when the Samuels project starts on the NW corner of Barry's Corner.