Not really; they're burning oil all the time because the seals need to be actively lubricated. And to the extent that "low emissions" can be claimed, it's achieved by burning the uncombusted fuel in the exhaust stream, which is cool but horrendously inefficient.

Then again, who knows: http://www.thedrive.com/new-cars/14064/mazda-confirms-rotary...

No and this may be inherently due to the rotary engines design.