If the QX1 will fire the shutter and save an image to the memory card without electronic lens communication, then it can be used with passive/manual lenses. A simple test is to confirm that a photo is actually recorded when no electronic lens is detected. You can also cover the lens contacts with tape and try shooting; if the camera captures a recognizable image, even if out of focus, that shows it can work with a non-electronic lens.

So the practical answer is: test whether the camera saves a usable image when the contacts are blocked or no electronic lens is attached. If it does, there is no obvious reason it would not work with manual lenses. Keep in mind that with passive lenses you would be focusing and controlling the lens manually, and electronic functions from native lenses would not be available.