A friend vomited into her cars aircon vent on the dash once while worse for wear. The phrase blowing chunks came to mind when she turned on the aircon a few days later. That car was no longer the chosen transport method for group outings.
Handy tip from the north, if it's cold, cats sometimes get up in the engine area. It might not be a bad idea if you know there are cats about to bang on the hood before starting the car. You might get something worse than the pee otherwise.
It very well may be either a fungal or bacterial growth in the A/C, especially if the odour developed over time. Sometimes it smells bad, sometimes - not, e.g. like a musk. The service can flush and clean the A/C and it's not really expensive as it's a common-ish problem.