IANAL but as I understand it (and have seen done by other smiths, dealers, and individuals) YES.
In a free state, a factory PGO "firearm" in 12ga, 20ga, .410, etc could be cut down to 14" as long as it came from the factory without a shoulder stock... and as long as you install the longer birdshead grip first, before assembling it with the newly-shorter barrel. I would expect to get jammed up by a LEO during an encounter with the weapon, however; if your barrel cut isn't exceptionally clean (factory look) a LEO will probably assume it's an SBS with no tax stamp despite your explanation.
In MA however this is a no-go. I know of at least one manufacturer who tried this method, but ran up against MGLs, the roster, and federal standards, and decided not to continue...
MGL definition is as follows;
“Sawed-off shotgun”, any weapon made from a shotgun, whether by alteration, modification or otherwise, if such weapon as modified has one or more barrels less than 18 inches in length or as modified has an overall length of less than 26 inches.
Because MA considers a pistol-grip-only 18" barreled weapon in 12ga (or .20ga, .410, etc) to be a "shotgun" in its factory form, adding a birds head grip and installing a 14" barrel or cutting down the 18" barrel to 14" would result in a weapon which meets the state definition of a "sawed off shotgun" - despite maintaining federal status as a non-NFA "firearm". Very steep penalties for possessing a "sawed-off shotgun" in MA.