It is done routinely on the ATR 42/72 thanks to a rather clever device called a propeller brake; engine no.2 (starboard) is kept running (at idle) but the prop is stopped. The engine thus acts as a pseudo-APU with no need for a real one in the tail cone - it's called "Hotel mode" (after a similar technique used on cruise ships). At most airports, however, a GPU is provided so that No.2 can actually be stopped (and so cut down on the noise). By then, however, PAX disembarkation/freight offloading is already underway from the port side.
Interesting to see from the outside the propeller stop fairly quicky whenever the prop brake is engaged!
The reverse is true on embarking/loading, when no.2 can be running already (PAX are saved a great deal of noise by the shielding effect of the airframe).
Not aware of any restriction on the use of Hotel mode during PAX boarding, but some ramp personnel object to working by the rear RH door for "Health and Safety" reasons
when Hotel mode is used.
Cheers