Depends on which type of "ich". Amyloodinium(called ich or velvet) is a dinoflagellate algae.Cryptocaryon is a protozoan.
Sterilizers only kill organisms in the water column;not those embedded in fish tissue or on substrate.
The lethality of a sterilizer depends upon the amount of radiation an organism receives relative to it's size. The quantity of radiation delivered to an organism is regulated by the wattage of the bulb in combination with the amount of time the organisms is exposed(dwell time or flow rate). Of course if you run a smaller sterilizer too slowly you are problaby not going to turn your tank over enough for it to be effective.
Bacteria and algae including amyloodinium are small and a sterilizer can be very effective. Protozoans including crytocaryon are significantly larger and less likely to be affected unless a well oversized sterlilzer is in use. Coralife turbo twist sterlizers include performance charts and recommended flow rates for various targetted oraganisms. It roughly goes like this for an 9w model:bacteria-400gallons per hour,algae300gallopns per hour,cryptocaryon 55gallons per hour.
So while the average sized sterilizer(7gallons per watt or so) is not likely to control cryptocaryon it will be effective against amyoodinium which is the more lethal form of Ich and possibly against secondary bacterila infection.