Installing a flanged vent, especially on EPDM, shouldn't be an issue with screw fastening. The flange is held down with compression and the typical installation is to use a butyl tape or other sealant between the flange and the roof material.
Screw holes would have little to do with leaking. If the flange isn't sealed, water will enter into the hole for the vent beyond the roof material. I would have more faith in attachment with screws into the roof deck than clamps to the vent hole framing. If screw hole leakage keeps you awake at night, covering the vent flange and screws with Eternabond tape is a very good solution.