Nope. To the best of my recollection BMW has not yet implemented variable vane geometry in its turbochargers. BMW turbocharging goes under the ubiquitous banner of BMW Twin-Power Turbo which is misleading. BMW engines can be:
Single-scroll, single turbo - eg 320d, 330d
Twin-scroll, single turbo - eg 330i, 340i
Single-scroll, bi turbo - eg M3, M4
Twin-scroll, bi turbo - eg. M5
Two-stage, sequential, bi turbo - 35d, 40d
Tri-stage, sequential, tri turbo - 50d (outgoing)
Two-stage, sequential, quad turbo - 50d (incoming)
VGT is normal on single turbo diesel engines. BMW is no different.
VGT has problems on gasoline due to high exhaust temperatures. Thus BMW there is using the next best solution. A twin-scroll turbo which BTW does not make sense od diesel.
Of-course on single turbo 3 cylinder engines or 6 cylinder with two parallel turbos twin scroll does not make sense.
But... AFAIK in the future for Euro 6d diesels BMW will offer non single turbo diesel engine. All will be twin turbo. That's their way to comply future RDE tests.