Gemmell already had four of the convictions when he was hired as manager in 2013.
Board member Joe Potangaroa said he did not know what would happen to Gemmell.
When asked whether Gemmell should stay or go, he said he "wouldn't like to comment" because he was not at the meeting.
Te Hauora is funded by the Wairarapa District Health Board with a two-year contract until 2015, said Jan McLaren, communications adviser at the DHB.
Gemmell was a former member of the Wairarapa DHB's Community and Public Health committee and a representative on the Te Iwi Kainga committee, which advises the board on Maori health services.
"We were very disappointed to learn about this event," said Dr Ashley Bloomfield, director of 3DHB Service Integration and Development Unit.
He said the DHB has written to Ms Pourau seeking an urgent meeting to discuss the situation.
When the Times-Age contacted Gemmell, he said he had no comment.
"It has been dealt with in court."
Gemmell was sentenced to four months' community detention, disqualified from driving for 18 months, after which he can only drive with a zero-alcohol licence, and banned from owning a vehicle for one year.