adding vegetables to rice in rice steamer?
Carrots I would steam or par boil first.
Frozen peas can be mixed with the rice or laid on top at the beginning of cooking.
Any type of dried bean needs to be soaked first and possibly short boiled before adding to rice.
Corn, diced broccoli, diced daikon etc - no problem
Raw carrots will actually need to cook, but you could even add frozen peas just at the very end of cooking so that they get heated through - they'll be fine that way. (a long way of saying why would it not be okay? It's your rice! (seriously, the taste will be fine and it won't hurt the rice in any way)
The carrots may still be firm (cut them smaller), but the peas should be fine. They're frozen and already flash cooked, so they really just need to be reheated.
Honestly, I add just about any vegetables to my rice cooker. I've also added spices, sauces, other grains... it's a very accommodating appliance.
With 'dry' vegetables like this, add them after you have added the right amount of liquid - assuming you add liquid up to x level. That way the additions won't mess up the rice to water ratio.
Frozen peas could be added later, but there doesn't seem to be much harm in adding them at the start of the rice cooking. They accumulate on top of the rice. Things like carrots should cook in the same time as the rice if cut small enough. Diced onion is best sauteed a bit first.
A (simple) rice cooker uses high heat until most of the water is absorbed. At that point temperature in the pot starts to rise, and high heat switches off. So regardless of the additions, it is the liquid-rice ratio that determines cooking time.