No, diplomatic missions be it embassies, consulates, or trade offices don't enjoy complete immunity. They aren't sovereign territories of the diplomatic mission.
The boundary wall of the embassy is the property of the host nation, and it's laws apply. The Embassy building itself is the property of the host nation. The space on which the diplomatic mission sits is under the laws of the host nation.
Raymond Davis is the perfect example.
Just because the Vienna Conventions states that the host nation forgoes the ability to unequivocally enter a diplomatic mission (Embassy. consulates and trade missions enjoy lesser freedoms) it doesn't mean that the embassy is the sovereign territory of the sending nation.
Lets say an individual enters an embassy with intent to do harm. The Security staff of the embassy can a) put the individual down, kill him/her, for which they are given immunity due to Vienna Conventions, self defense. or b) subdue the individual and hand him/her over to the local authorities that will try him/her to under greater degree of the crime.
Edit; Jullian Assange, is the prefect example.
Remember anyone can do tit or tat, unless the Americans want the Pakistani Embassy to start cutting down trees on their sovereign territory, which it cant by the way because well take a look on Google Earth, this 'incident' will be resolved under the table.