If you have a working refrigerator, you can convert it into a grow box, and yes you can use the cooling system to act as an air conditioner for your plants. I have done this conversion in different types of refrigerators and all worked well.

Obviously it's not a simple project, you'll need to wire the compressor with a new thermostat to control the temperature in the fridge, and you'll also need to install ventilation ducts to exhaust the heat from the lights, without exhausting the cold air from inside the box. Attached are images of a prototype I put together 2 years ago (GE Refrigerator, top freezer/bottom fridge conversion). The heat of the 300 Watt LED Light is exhausted through a separate section in the roof. The same concept can be used with a Cool Tube using HPS or MH. All you need is 2 ventilation ducts to exhaust the heat. One duct brings the outside air into the tube, and the other brings the heat out. You must be very careful not to drill your ducts through a refrigerant gas line.

I have a lot of experience with these type of conversions, and could sit here and write pages and pages about it. If you plan to do something similar and need help, just ask me your questions and I'll reply.