In this case, yes, because it would still be part of the base set, but different. (They would still show up on the Collection Summary and add/update pages for the base set as well, which I forgot to mention before).
This set seems unique in how it was issued. As such it doesn't seem like it conforms to the norms. There's always (at least) one...
VERY slow trading due to health problems. Not transferrable so safe to trade with, just moving is painful and can't always access the cards.
Cardboard History My COMC
New Collection Website: Cardboard History Gallery (Still under construction)
Tips on how to make your scans look like the card does in hand (No more washed out, fuzzy scans!):