Can a US airline add an employee passenger as crew?
First of all it depends on what type of "employee" and if the jumpseat is in the cockpit or the cabin.

According to the answers to this question there are no regulations on who may sit in a cabin jumpseat as long as it meets the specifications set out in FAR § 121.211 for proper airline seats. So the airline is free to set policy for cabin jumpseats.

As for jumpseats on the flight deck the restrictions are quite stringent. If the employee is a pilot FAR § 121.547(c)(3) allows off-duty pilots to fly in a jumpseat on the flight deck, so there would be no need to make them an active crew member.

FAR § 121.547(a)(1) allows an on-duty flight attendant to fly in a jumpseat on the flight deck. The person would have to be a certified flight attendant, so you couldn't just make any employee a crew member. Remember also that flight attendants have hours of service restrictions, so any time they are considered on-duty has to comply with the h.o.s. regulations. 

Certain other types of employees are allowed to fly in the flight deck, but they have to be performing a specific function on the flight that requires their presence in th cockpit. For example, a mechanic could fly in the cockpit if he's there to monitor something on the aircraft. A flight dispatcher could be on the flight deck if they are observing flight operations as a part of training. 

Even some persons who may be given access to the cockpit for operational need, like air marshals or training personnel, still must have a seat available in the cabin. 

So they can't put someone in the cockpit just to transport them from place to place and they couldn't just plop a salesman or a ticket agent there and say they are a "crew member." 

There are regulations stipulating the minimum number of flight attendants on a flight but not a maximum number. So, technically they could make a flight attendant part of the crew, but if that person was just listed as a crew member and wasn't actually performing any duties, the FAA would certainly interpret that as a violation.