The way we are set up in my house is, we have one xbox in the living room, and one xbox upstairs. My son and myself alternate between the two xbox's dependent on who else in the family wants to watch the TV. We use my xbox live account on both consoles and games are saved to the cloud.
I play on online games, but my son doesn't, he just plays on games like LEGO Batman.
So my question is, can we both be playing at the same time on the one Xbox Live account, but with me playing an online game, and he playing on his single player game on the cloud?