Yes, that's what my '83 300SD does.

With the DS door open, just inserting the key in the ignition lock will not activate the buzzer.
With the DS door open, inserting the key in the ignition lock, and turning it CW will activate the buzzer...then if you turn the key CCW back to the zero key position the buzzer will still sound if the DS door is open.
Partly removing the key about 3 mm will silence the buzzer.

Leaving the parking lights, or headlights on, will activate the warning buzzer when the DS door is open...whether the key is in the ignition lock or not.

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78 W116 300SD 'Desert Rose' new as of 01/26/2014
79 W116 300SD 'Stormcloud' RIP 04/11/2022