You are extracting fermentables from the rice. The enzymes in the malt will convert the rice starch into fermentable sugars.
But you are right, You can add the rice, raise temp to the correct strike temp of your grain mass/temp and then mash in.
Its also important to grind the rice up prior to cooking, can you coffee grinder or food processor apparently. You want the rice to be in in small pieces to maximise surface area so the enzymes can get to it easier.
It can also help to extend the mash out to ensure good conversion and you need to remember that the cooked rise will not absorb any water in the mash tun as it will already be saturated.