No, because pistols aren't allowed to have a shoulder stock.
If you welded the mag, you could have:
a PISTOL, built upon a receiver which has never had a stock attached, with 7-1/2" upper, flash suppressor, bayonet lug and handguards, but NO stock of any kind, and the 50oz weight limit does not apply. or;
a RIFLE with a barrel 16" or longer, flash suppressor, CAR stock and bayonet lug and flash suppressor. or;
a SHORT-BARRELED RIFLE (SBR) with 7-1/2" upper, flash suppressor, CAR stock, handguards and bayonet lug.
The SBR with welded mag would give you the configuration you want, but an SBR is a Title 2 firearm like a machinegun. It has to be legal to possess an SBR in your state, and you'd have to submit an ATF Form 1 (application to make an NFA firearm) in duplicate to the ATF with a $200 check for the making tax, and fingerprint cards and photos, and get your local sheriff or other "Chief Law Enforcement Officer" to sign both copies. If you can get the Form 1 application signed off, it's been taking 3 to 6 months to get them back approved, at which time you could make your welded-magazine SBR.