yes, yes ,yes that will work.
your expelled hot air is being drawn back into case and not expelled into your room. you have too think of the pc case as a very small grow room/tent.
if you want even more crazy, you could use a aero system/hydro system in a full tower system case. but thats another crazy idea.
i personaly would add a fan too rear of cab, this will draw any hot air in the cab (not pc case) out and help draw cool air in too. naving a cab inside a cab means you have too look after and vent two spaces.
i would also search forum for anything mentioning pc case growing. check others ideas and problems, this way you can put all the best ideas into one case. ideal things would be: mini carbon scrubbers, homemade co2 gens, SOG/LST.
having a small area requires a smallish plant. you cant be putting in a plant that when full grown is 5 foot high into your 12/14 inch high pc case. so selection of strain will be important too. you want atleast a smoke for your high amount of effort. looking into the lowryder strains these grow around 12-14 inch so can/could be grown with some tender LST or a SOG screen.
Tamzi