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A problem with the booster - a vacuum leak - would cause a higher idle, not lower.
With the AC compressor on, the engine idles with a bit more power (slight air/fuel adjustments via the ECM) to compensate for the additional load, hence why this behavior doesn't occur with AC on.
I wonder if the DCT is engaging a bit when the brake is depressed, like with a conventional automatic, and this load is causing the idle rpm drop. It is probably normal or at least causing no damage.
I don't have an M3 but I would put it in N to see if the issue goes away. (I hope to get an M3 one day, so I like to read up on the technical issues that pop up)
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