Yes, that's correct. The buzz is there when the key is in off position.
I've tested this some more and here's what I found: when the engine is cold ... like in the morning, the buzz is loud and prolong for minutes; when engine is hot, the sound is equally loud but just lasted a few seconds. The buzz/hum noise ends which a "tac tac" sound ... like a relay.
By the way, where is the ABS relay? I've replaced the front rotors on the car recently ... could it be related?