Yes, if a cop invades your home without following proper procedure (i.e., by announcing "this is the police" or by wearing police uniform), in a state with castle doctrine you can shoot trespassers without attempting to flee.

Both the castle doctrine and stand-your-ground doctrines let people shoot attackers without attempting to flee. One of the big differences is that castle doctrine only applies in your home (but is a very strong defense that is generally acceptable in almost every state), while stand-your-grand would apply outside your home, but is more limited--not every state allows for a stand-your-ground defense. For example, California allows for the castle doctrine but not stand-your-ground, so you would have to reasonably attempt to flee before engaging in deadly force.