It really does depend on how the routers and systems on the network are configured.
At our office, our machines will not connect to the local domain due to the collision in MAC addresses. You'll get a notification message (in Windows) saying there is already a system with the Id on the network.
Sometimes you get into "races" where each computer attempts to register itself with the router, and any traffic coming to the machine can get lost since packet A will go to your machine, the other machine will register, so packet B will go there. Things can start bouncing back and forth.
You can start seeing unreachable host errors due to the collisions as well.
The results really do vary depending on when the duplicate machine is coming online and how the current infrastructure is setup to handle such items.
Your network admin will have more detailed answers on this.