The buzzing is usually from too low a PWM (pulse width modulated) frequency used to drive the IAC (Idle Air Control) valve.
The Adaptronic has different values for this, unplugging the IAC will only give you the fastest idle available on the car, it doesn't solve the tuning discrepancy you're experiencing.
If the unit has been tuned by a shop, you really should be taking it back for them to adjust the settings to a more comfortable level. IIRC 785 Hz is whe're the NB's run their IAC valve best (it's around there, the exact frequency is escaping me, but not hugely important)...
Clicking or buzzing comes from too low a frequency, NB's hate anything under 500Hz and some are even comfortable around 1000Hz (but longevity of IAC id degraded at those frequencies).
If you want to tune it yourself, read up on the Adaptronic manual on how to tune your idle settings,
this is a good guide but i would be holding the tuner to ransom over it, if you have time.
Also, chek your adaptronic plug in harness, to see if the right year model has been supplied for use with your car. For exapmle a 99-01 harness will function on a 02-05 NB, but soem wires are transposed. Same for the early 1.8s (94-95) have a couple of wires in different spots when compared to the 95-98s...