Already being done with the PPS-43s. Folding stock is welded in the folded position so that it cannot be opened up into a "stock".
http://centerfiresystems.com/pps43-pis.aspx
The "pinning" might be an issue if the pin could be very easily removed. I said "might" because my AR-15 pistols could easily be converted to SBRs by the simple swap of a buffer tube and addition of a stock...but that requires more than the simple knocking out of a pin. My Dracos have trunnions that are already set up for underfolding stocks, so installing one and welding it in the closed position could conceivably do the same thing.
The only problem I see is that the PPS-43 comes from the manufacturer/importer with the stock already welded. If you drilled out the trunnion holes (or mounted a folding mechanism on the rear plate of the Draco) once you mounted the stock, you would have an illegal SBR
UNTIL you got it welded up. If you had a way to weld the whole lashup together before mounting it, you would not have to worry about it at all.
It would be considered a "pistol" under federal law; whether your state and local gendarmerie agreed would remain to be seen in the light of their rules. Some states regulate pistols separately.
My question would be why do it since you can't actually use it and it just adds unnecessary weight. The answer, "because I just think it would be cool", works for me, but I can't think of it being cooler than a Draco pistol by itself. Now an SBR...? Yeah...