Feeding an outdoor cat?

We have an outdoor cat that comes around our doorstep. Very sweet all black, adorable. Our cats only stay indoors because we live in an area where there many coyotes at night. Since discovering a rodent problem in our outdoor water heater closet, we thought this would be a good extra measure to keeping the rats away (in addition to traps & sterilization). So we feed it, and it hangs around our back patio (which we share with a disapproving neighbor). I think its a great idea, but I'm wondering if there are any down sides to doing this?