Since it expels a bunch of air you'll need to work out some baffles to provide good airflow from the closet. Maybe a zig-zag of panels? At least it'll be low dust.
And, wild thought, you have a large supply of dust free air - let that pour over a workbench or exhaust it into a booth and you now have a dust free place to do finishing! If you go with a booth, line the booth with rock wool and it can be your baffle.
Also, it's not just the high end - dogs get unnerved by low rumbles, so isolate the DC from the frame of the house if you can.