Well, it is kind of weird. If you are hired by Coca-Cola, you cannot continue to work at PepsiCo. No organization would ever allow you to continue to work after being hired by a direct competitor. In fact, most organizations will escort you right out the door without allowing you to give two weeks notice if you are going to a competitor, but in this case Smart is asking him to stay longer.
If Key agreed to allow Faulkner to stay on through the bowl game, then that is the only reason I think this can being allowed from our perspective. However, if Faulkner agreed to start right away, then, No, he should not be allowed to consult for the bowl game. While there may be benefit if he can continue to gather intel to bring back to our team, the conflict of interests here are pretty glaring.