Maybe you can't play the same game (I haven't tried) but it is definitely possible to let your kid play other games. I have this very setup with my son and it works. An other advantage to this setup is that you can select which of your games to let your kid play.
I don't know, we've been doing it for years. Maybe it's a regional thing? One account for me and one for my kid. I authorize the use of my games for his account on his machine (I need to login with my account on his machine to authorize his machine, I did it just the other day as the machine authorization only seems to last for a while). Then he can install and play any game of mine I allow (or all) once he logs back in with his account.