Hello,The lack of power without fault codes is often caused by faulty boost air temperature sensor. It can be showing that air is too hot to the ECU and this will limit boost pressure. Please have it's actual values checked with diagnostic computer and replaced if neccessary.
but will that cause the engine management light to come on?
Yes it can. When this light is on, there is a clear fault code stored in engine control unit, which must lead the workshop to the faulty component. If possible, please let me know this code to help you in the best way i can