Other than lack of cooling ,will a failed ac compressor on a 2006 Volkswagen Beetle cause other issues if not repaired? it is a convertible.
It depends on the cause of the failure. A rattling compressor clutch bearing could eventually disentegrate and throw the belt off leaving other things in the lurch or causing damage to other things under the hood.
If the problem is internal in the compressor shell (noisy when engaged and so on) then there is the possibility of a compressor coming apart same as the compressor clutch scenario.
If this is the case and there is no fault with the compressor clutch bearing then the compressor can be unplugged and run like that with no problem.
One downside of no compressor operation is that the DEFROST function may not work well as the compressor is used to dehumidy the air in the cabin and prevent window fogging. This will vary car by car so there is no way of knowing how bad this situation would be.