It depends on how it failed. If the magnetic clutch burned out, which is what smoke suggests, the compressor will not run. Besides the AC mode, it also runs in the defrost mode to remove humidity from the air so it doesn't condense on the cold windshield. You may experience minor fogging at times.
If the compressor locked up, the clutch or the belt would be slipping. Either one could cause smoke but the belt would also squeal loudly. You can run the engine like that as long as the clutch doesn't engage. That means not using the air conditioning or the defrost mode. The easiest way to keep the compressor from running is to remove the compressor relay, then you can switch to any mode including defrost.
If the clutch locked up, the compressor would run all the time. That wouldn't usually cause smoke so it's not likely that's what happened. That would reduce fuel mileage a little, and it might reduce the maximum temperature of the air in the "heat" mode a little.
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Thursday, October 3rd, 2013 AT 12:33 PM