To the above...
"Yeah"... I see your point "sort of" and "Naah" I see the opposite point "sort of"... I think it's a delicate point that could be made either way.
If you shoot 37mm *cartridges* with anti personnel loads directly thru the 37MM tube... it's a DD as per the BATF. No questions about this.
If you shoot 12 Guage cartridges thru a 12 guage barrel that is used as an adapter to the flare launcher, you are shooting a 12 guage short barreled shotgun. The adapter itself might be the SBS. Or the launcher/BB combo might become a SBS and not a DD as it does not meet the bore size requirement for a DD. Or at least it could be intetpreted that way.
Methinks a BATF opinion would make this one go away.