Is a vent really necessary if growing in a small closet?

lets say 4 plants with one 600w light in a room with no furniture and a window adjacent to the closet that can be opened

a 5 inch fan would be nice to exhaust, any open spaces will suck air, being a passive intake. Ventilation plays a huge role in yield %.. http://botanical.com/hydro/air/calculating_fan_requirements.html just do it don't make the mistake of cutting corners

How big is the room?

depends if its a big window keeping cc02 temp and humdity right
and if any passer by grasses you to the feds as you have no CF

also no light in your 12/12 cycle will be tricky

If you have no new air going in the closet yes. The plants will eat all the co2 then stop growing within 1 hour of lights off. You need to add a co2 generator or let fresh air in.

far as im aware you dont need c02 in lights off but moisture build up will give you bud mold very quickly

I still get some times mold with lights off with a big extractor on

A window in the room does no good to a sealed closet.
If you don't put a vent/ exhaust, how do you plan to control your temps and humidity?

yes your gonna want one will make things much more simpler in the long run