If an engine is supplied test cell run then the approved MM on the FADEC equiped Boeings I work on says that you need only to do a idle leak check before releasing it to service. On the older Boeings there is of course the part power checks and the take off power checks to do. This may differ from operator to operator though. I personaly like to make sure that the engine accelerates and it can go into reverse.
My logic being is if the engine won't go to full power the pilot will abandon the take off and come back to kick my a***e. Embarrassing but not tragic. If the engine won't go into reverse on a wet, short runway that is a whole new leval of embarrassment!
I have never changed all four engines at once though and the times I've changed both on a twin we did an airtest but that was part of the refurbishment we did any way.
Rgds Dr I