Yeah you can set up a private room and have people 'join you' in your room.
Private rooms have voice-chat between races. You talk near the Gamepad's microphone to engage.
However, if you wanna have some fun with friends but still have strangers online racing, then just join a buddy that's already racing. You'll join up in the next available race and see them, while at the same time still being able to race other strangers.
There's no voice-chat in this mode, however.