Can I use a rice cooker with flavored rice boxes?
It is possible to use a rice cooker to prepare rice from boxes but it is not optimal. These box rices typically call for the mixture to be first browned in butter before adding water and flavoring because it is not all rice. There are bits of pasta in the mixture too. The rice cooker is able to cook it but the result probably will not be as good.

It is very possible to flavor white rice with seasoning. I often like to flavor my rice if I plan on making fried rice or if I am lazy and don't feel like making anything but rice. If you want to imitate a specific flavor, you need to first find out exactly what that flavour is and put that seasoning in the water that cook the rice. Often though there might be some flavors that can't be added until afterwards. Such as the cheese flavored rice you mentioned. Cheese and rice cookers don't mix. You would make the rice then later add a cheese sauce that you made.

Please note that one main difference that might occur is slight difference in moisture content. From the box rice I've made on the stove in the past, I know it is a bit more "wet" than rice made from a rice cooker. In my answer here, I explained how a rice cooker works. Essentially it will continue to cook until all the water has boiled away.