A third arm would not simply add one more limb. The nervous system, skeleton, muscles and brain would all need to coordinate it.
What changes first
A third arm could provide major advantages for manipulation and carrying, but it would require a redesigned shoulder structure, extra muscle and new neural control. Evolution would also have to balance the energy and developmental cost of maintaining the limb.
The physical or biological constraint
The scenario should be treated as a thought experiment. Where the consequences depend on unknown parameters, there is no single precise outcome.