Yeah, you need quite a bit of low end torque to do a burnout in an automatic. You'll probably have trouble doing a burnout even while doing a brake-torque like epj3 described. The problem is that you don't have a bunch of low end torque at less than 2000 rpm or so and BMWs have tight torque convertors that aren't going to allow the engine to rev up much with the foot on the brake and the gas floored. Without the ability to get the RPMs higher, you won't develop the torque you need to do a good burnout. My friend and I tried many times with an automatic E36 318i and an automatic E36 325i. We could never get either of those cars to even chirp the tires no matter what we did (we actually ended up blowing up the differential in the 318i). My automatic Camaro will smoke the rear tires by just flooring it without even brake-torquing it, but it has gobs of low end torque. Burnouts are all about the torque.
And for the record, brake torquing an automatic is easier on a car than dropping the clutch in a manual car. When you brake torque an automatic, you are loading the drivetrain gradually. When you drop the clutch in a manual, you are hard shock loading a previously unstressed clutch, transmission, driveshaft, u-joints, differential, and rear half shafts. It's very easy to break things with that kind of shock loading. Think about the strain you put on those parts by suddenly engaging a crankshaft rotating at 4000+ RPM to all of those stationary parts. Think about the forces and harmonics you instantly place on your crankshaft and crank bearings. Ouch!