Without turbo/boost it will work like naturally aspirated engine. So it will work but with less power. Like said earlier you likely have a cracked exhaust manifold which can explain most of the symptoms. You can do a rough check on turbo vacuum actuation just by checking if the rod on vacuum solenoid pulls the guide vanes closed when engine is started. (This can be seen without taking anything apart from above with a flashlight.)

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E39 530dA -02 M-Sport Messing metallic
E53 X5 3.0dA -06 Sport Stratus grey