Doesn't really track if you ask me.
The Protostar's registry suggests the ship was built at least 2 years after VOY disappeared... and its an NX class (experimental).
VOY didn't make contact with SF until the 4th season (2375).
The appearance of the Janeway training hologram and the fact the show is set 5 years after VOY returned home (aka, year 2353) suggests to me this vessel was equipped with a bunch of tech VOY brought back from the DQ after the ship returned home (a product of a couple of years of SF/UFP R&D most likely... and since there are over 150 member alien worlds in UFP, coupled with the fact they can just tell the computer 'analyse technologies VOY brought back from the DQ, contrast with VOY sensor data, latest in UFP scientitific discoveries and come up with a way to make them functional'... the computer operating at superluminal speeds would be able to EASILY come up with new technologies in a few weeks to a year most likely (given that SF HQ probably has its own version of a 'supercomputer')... choose the Protostar (which could be one of several NX class ships chosen to house and test these technologies) and launched it with the Janeway training hologram.
Its possible the Protostar was equipped with these technologies so that UFP would send exploration ships to the DQ and other distant parts of the Milky Way as a next stage in exploration.
Next order of business, while the ship was testing a new method of FTL (possibly Transwarp, Enhanced Warp drive, Coaxial Warp or Quantum slipstream), there was an unpredictable event which caused the ship to veer off course... with the FTL drive speed going into 'overdrive' and causing it to lose contact with SF, eventually crashing in the DQ.
The existence of other AQ species in the DQ could be explained by the Caretaker pulling in ships before VOY (the Equinox was already in the DQ before VOY, as was that Cardassian ship), so it stands to reason a civilian transport ship was probably pulled to the Array... or they were caught in a wormhole or something else.