I don't know if you remember a thread of mine you replied to, about my ex... just reminding you, so you know where I'm coming from, that I haven't lived through a rehab attempt, recently came out of a relationship, and that I've got a possibly controversial take on codependence that probably many here would feel comes from lack of awareness or experience.
If you're seeing what you think is a genuine commitment to get help, and you can live *comfortably* without the money without expecting to see it again, AND it's only for 2 or 4 weeks... I don't know, it's a decent thing to do. I can't comment on how realistic a proposition it is - no one can, really, I think. It sounds as though you and his sister feel he's serious.
I don't know what else to say. Seeing someone you have loved fall out of the web of normal human connection is a nightmarish prospect to me. Equally, being the last thread is a terrible obligation, emotionally if nothing else. (Do you feel that pressure, even though you're NC, and your contact now is through money?) Are you able to talk to his sister about this?
Can you handle your own responses to this, and release yourself from the outcome of his rehab?
(last question - is public transport prohibitive, where he is? am guessing so, just checking - otherwise, a taxi does seem a bit luxe... but the rent for the 'sober house' seems like a good and kind and reasonable thing to offer, in the scenario you're describing...)