I have a new M3P with 1400 miles on it now and no, mine does NOT sound like that. Its much more quiet and doesn't have an "uneven" sound like that. The pump/blowing sounds out of my M3P when the car is stationary/locked are smooth and don't sound "grumbly" like that.
When my M3P is in track mode, its MUCH louder, but still doesn't sound like that. I'd make an appointment with Service for them to check it out. Someone on Reddit posted in the M3 subs as well with a similar bearing type noise like this but it sounded actually worse than yours. Seems like some faulty pumps/motors were installed.