attach some ducting on the inside and then over to the other side of the cupboard so that the air is being drawn across the closet and yes it would work fine.
Sure mine is I have the exhaust at the top of the closet and the holes at the bottom. Just with a passive intake you need to have about two times the hole size as the exhaust.
Once you have this number if you plan on adding a carbon filter to the system aswell you need to add 20% for the reduced efficiency of the carbon filter attached to the fan.
Are you using CFL's or HID's?
A passive intake should ideally be located at the opposite end to your exhaust to allow good airflow movement through your room. BUT as Tip Top Toker has suggested you can use ducting to direct the passive intake wherever you need it to be. This is what i do in my flowering Closet.
Sure mine is I have the exhaust at the top of the closet and the holes at the bottom. Just with a passive intake you need to have about two times the hole size as the exhaust.