First thing you need to think about is how you are going to get air that is hot out of that closet through ducting and out of the apartment.
Because without doing that it's just going to
get too warm.. plus a filter will not remove 100% of the smell if its just recycling the same air.
Plus the humidity will keep rising and moisture will drip off the ceiling..then your filter will work even less.
Plus without air exchange your co2 will diminish.
I say this because you are talking about a sealed closet..
Doing everything it takes to run a grow properly , either a sealed one with dehumidifier, scrubbing, added co2, or a non sealed one with an active air exchange. Will be noisy , so regardless of the smell it's not going to be secret to people living in the same apartment.