Actually you can. I've been playing with Hangouts and my wife's phone; here's what I found, you have to go back to old school hacking with GV.
Go into the GV app and set the phone to receive text messages via the messaging app and set hangouts to receive messages for the phone. When someone send a message to your GV number it will show up in hangouts as coming from a strange number, this is the GV alias number for that person. Save that number in your address book as an extra number for the contact, then send your SMS messages to that number rather than their actual cell number. GV will handle the back end translation for the other person and your text will magically come from your GV number.
Hopefully this all makes sense, but trust me, it works. The only thing to remember is that if you aren't on Sprint and you try to send an MMS to this number it will disappear into the internet black hole that is GV. Sadly, despite people pleading for it for years, GV still won't handle MMS messages.