If you form a corporation and that corporation manufactures (form 1) or purchases and transfers (form 4) that weapon than any member of the corporation that is listed as an allowable officer of said corporation may use the gun. This person should have a photocopy of the Form 1 or Form 4 and paperwork showing that they are an authorized officer of the corporation that owns the weapon.
Otherwise, no. For anyone to use a 1934 NFA gun, that your name is on the paperwork, you have to be present with them. If you loan an NFA gun to someone, and they take the gun out of your presence, they are in illegal posession of a gun that will send them to the Federal Bureau of Prisons for one or two decades.
It depends on the route you go to get your tax stamp for the NFA item. If you get your tax stamp with a CLEO sign off then the answer is no. No one else may touch/handle/borrow the item. If you choose to do a trust, then any trustee of the trust may legal use the item. When you get a NFA item and tax stamp with a trust you do not own the weapon, the legal entity, "the trust" owns the weapon. Would be no different than if you worked for a private security firm that had class 3 items. If you were and officer of that company or had documentation stating from an officer of the company that you were allowed to use the item it would be legit. I think this though is rarely enforced as you see plenty of youtube videos of groups of people at the range taking turning with the toys. I would guess that if you got on the wrong side of the law and they wanted to make an example of you they could.