The HVAC consists of directional air flaps that mix the air through the heater core and the air conditioning evaporator and the fan to move the air.
Provided its just the heater core that was the problem, I would think your aircon will work just fine. You will only be getting fresh air and chilled air now though, without much mixing, so it might blow a little cooler on occasion when it would otherwise mix with the heat.
2001 Audi S8 - Solar Sunroof, heated front and rear seats (just what you need in Australia!) Tinted side and rear glass, RNS-D, XCarLink, Bose, clunky old phone in arm rest!
1997 Audi A4 Quattro - 5spd man "Hamilton's Club Sport" - will miss the old girl!