Wow, there is a thought.
I would highly highly recommend that you build a small enclosure. Floor to ceiling 2"x4"s, 1/4" drywall, large shop vac with dust cover hood (easy to make...and use dryer duct to connect the exhaust air outside or back into your enclosure as it will still have dust, the smallest powdery type)...this will cut noise, reduce dust, and help keep you in the apartment.
Once you get that build up of dust in the carpet it is unlikely it will ever come out, once the dust gets into the ductwork it will collect more moisture, and it will in general cause you so much grief...in this case a measure of precaution will pay for it self 10 fold.
Just a series of thoughts...best of luck with your project