Adding uncooked rice to a slow-cooked stir fry
You can certainly add rice to the slow cooker--but it will end up more like a rice stew, rather than a stir fry ("slow-cooked stir fry" is also an oxy-moron--the recipe that you link to is in fact a vegetable and meat stew with a vaguely asian flavor profile and has nothing whatsoever to do with a stir-fry). However, the rice you cook in the slow-cooker for several hours will be gummy, overcooked, and the starch that the rice exudes will make the whole thing a gloppy mess, more like a badly cooked risotto than anything else.

My advice would be to cook the rice separately. If you really want to cook the rice in with the other ingredients, I would add it as a top layer, so that it steams rather than boils. But, again, it seems like a much better idea to cook separately--you can even make it in advance.