Just to be clear on this:
The Leica M9 is not a "Mirrorless interchangeable lens camera" in the sense that matters, IE. Live View off the sensor to compose and focus. It is a digital rangefinder, nothing more or less. All you Leica fanboys can stop saying M9, we get it, it has no mirror but it doesn't do the "mirrorless camera" thing that the Olympus and Sony cams do.
However, the Leica M (240) is exactly what the OP is asking for; does LV off the sensor allowing adapted lenses to be precisely focused. It's *also* a digital rangefinder at the same time.
The first non-rangefinder mirrorless? Probably Sony. Their E-mount for NEX cameras is already sporting a FF sensor as a camcorder. Just need to adapt it to a still camera form factor.
Oh, and I handled an RX1...doesn't seem particularly like other digitals to me. I liked it!