Don't see why it wouldnt work. The main thing I see with those filters is they go black with carbon dust, so that would go all over the bottom of the cyclone. As long as you washed the clear bin and filter cover (which you need for the cyclone to fit) you would probably be ok.
Oh, and the noise will be much louder, the filter provides good sound deadening (try it!)
Failing that, filter pads are only a couple of pounds, hepa filters only a fiver, change every year and job done!