Sure they could.
But, wouldn't they be better off having another helicopter or aircraft just follow it since there are no hostages on board.
How do they know the helicopter pilot is a bad guy? Maybe the pilot's wife and small son are being held hostage themselves to make him fly the bad guy out?
So, the cops may not want to shoot the pilot without knowing for sure that he is a felon whose escape would most likely lead to serious bodily harm or death to a third party.
Maybe you could have a sniper disobeying a commander's orders to shoot the pilot because the sniper suspects the commander is in with the hostage taker on this caper?
The bottom line is that you are writing a fictional story. Run with what you think might sell.
By the way, are they going to shoot the pilot with a .223 or a .308?
This career is not a sprint, it is a marathon.