we do have a client who has had to delay launch of their mobile site as their devs have hit a snag, so we should be able to get quite an accurate picture of what happens to not mobile friendly, then what happens when you make responsive.
For them, visits yesterday were down by about 8% on an average Tuesday, which appears to be all driven by a 20% drop in mobile traffic. Which sounds meaningful, but the figures were down by almost exactly the same amount on Monday.
I do wonder how much of their mobile traffic is brand, and how vigilant Google will be about demoting the brand site for obvious brand queries (like location searches) - this site is both retail brand and factory visit site - so it could make a big difference to figures. I think once we have a weeks data I'll try and do some analysis of location/device/landing page, but so far I'm still not sure we're seeing an impact, let alone able to look at what it is!