final A/C questionb (I hope, god I hope)

Long story short need to cool a very hot 8x8x6.5. It has a window. Can I or Can I not just place a standard window AC unit in the window that goes outside and run a sealed Co2 system? So my theory is air goes around outside like normal, cooling the AC and the air inside is pulled in past refrigerated coils and blown back in the room right? What a time this is becoming. Thanks for your time and answers
 
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