Nope. You have to actually break or disable something to enter the premises or property for it to be breaking and entering. Hence the "breaking" part. Being on private property with the intent of doing something unlawful is criminal trespass. That's where the notion of having to tell someone to leave if your door was unlocked comes into play. Your drunk neighbor comes stumbling in because the door is unlocked and he's inebriated to the point of getting his house wrong. You shoot him. Cops come, find his car full of beer cans, no sign of forced entry, and no weapon. Who do you think is in trouble now?

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-Dik