I think it's widely understood that transposing every occurrence of 'schon' into 'already' frequently results in un-idiomatic English, or 'Denglish' as in #14. (There's another recent thread about this in the Translation Correct? forum.)
This to me is a clear case of that, just going by my own Sprachgefühl as a native AE speaker. It's not easy to clearly articulate the rule or principle involved, though.
'Yet' seems better, but I don't think you need a 'yet' here either. "Are you still drinking, or have you started living?" expresses the meaning. Further variants including extra flavor or emphasis, as a nod to the role of 'schon,' might be "Are you still drinking, or have you finally started living?" or "... finally decided to start living?"
The IKEA slogan feels harder to translate into a catchy English phrase, because the wohnen/leben contrast is hard to express without sounding a little stilted. "Do you merely inhabit your space, or do you live in it?" "Stop existing. Start living." Those aren't quite right.