So, do you think when Scotty mentions his "prize beagle" the assumption is that Archer's no longer alive but his beagle is? Maybe if Archer had died a few years earlier or something. Hm.
It's not even clear from dialogue that the beagle
is alive, let alone Archer.
Suddenly, I'm getting an image of a statue in front of the President Archer Memorial Institute of Theoretical Engineering at Starfleet Academy, or maybe in the lobby—Jonathan Archer as a starship captain, with faithful beagle at his side—and Scotty just "borrowed" him temporarily, thinking old Porthos would be back in place before anyone noticed he'd been missing.
Except wasn't the Scotty's test specific to bio-matter?