Dave,
Actually no, United Airlines says it flew one of its 787s to a Boeing facility in San Antonio on Tuesday for the battery fix it needs to resume flying.
United (UA) #6850 ? 23-Apr-2013 ? KLAX - KSKF Flight Tracker ? FlightAware
So your are only allowed to fly a grounded aircraft when you want to.
On a side note, today the FAA estimated the cost to fix each ac is $465,000. Quite the box