This camera seems - at least on paper - as the street photographers dream. A small body / large sensor package.
However it is missing a real optical VF option, a must for quick paced street use. They also have no mention of improved shutter lag - or lack of it. Sort of defeats the purpose ?
You've posed a very interesting question. I sometimes use a G11 for street photography, but it is not ideal because of some of the issues you mention - shutter lag, slow lens, lack of a decent view finder. To top that, the inability to separate your subject through blurring the background is a challenge.
The G1X will hopefully fix the last problem to some degree, but having a smaller than APS-C sensor and a very slow lens at the long end, the depth of field will still be quite large.
I doubt that the shutter lag can be eliminated, because of the use of the back screen for framing - you are essentially shooting in live-view mode.
On the other hand, you will have the benefit of being unobtrusive.
I don't think it will be perfect for street photography. On the other hand, it will not be useless for that purpose. The slow lens is probably my biggest concern. With enough practise, you can compensate for shutter lag, but you cannot compensate for the slow lens.