yes hyeung it would still be able to accelerate and from what you described it won't. It's not the turbo. Any competent technician (especially a BMW trained one) could tell you that.
Here's some food for thought. I have a 2002 Ford F250 4x4 diesel and on very cold mornings (35 and below) there is a bypass valve that will allow the boost pressure to bleed off rather than fill the engine. This is done to avoid damaging a cold diesel engine. Diesels run very cold temps (compared to gasoline engines) and take forever to reach a normal operating temp on a cold day. The boost is bypassed while warming so as not to load the engine while cold. I can pull out of the driveway and for a couple miles there is no boost. I putt along and just as I reach the heavy traffic the engine has warmed and now the boost will build. The point is, your engine still makes power regardless of turbo boost. If the turbo was not making boost you should still be able to accelerate. Granted, it will not accelerate near what it does with boost but it will accelerate. Something is going on with your car relating to load sensing. I say this because once it reaches 3k it runs fine. It could be a cam sensor, a boost reference sensor etc. Honestly, with my years as a bmw tech, I never came across a bmw diesel and that's probably the problem with your dealership. However, it's not rocket science especially if you have the car in front of you. They should be able to diagnose the problem and fix it. Diesels are actually quite simple and you don't have an ignition system so that's one less thing to worry about. All that you need with a diesel is air and fuel. Good luck.
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