I thinks it safe to say Gore isn't running. But there are historical examples where a deadlocked convention has reached out for another candidate:
1852 Democratic Convention
Baltimore, Maryland
June 1 to 5, 1852
Nominated:Franklin R Pierce, of New Hampshire for President
Nominated: William O Butler of Kentucky for Vice President
The democratic party opened its convention in Baltimore in June of 1852 with four competing candidates for the Presidency. Most of those who had left the party with Van Buren to form the "Free Soilers" had returned. Before deciding on Presidential candidate the convention adopted a platform designed to unit the factions fighting over slavery. It opposed any further "agitation" over the issue of slavery. When it came to selecting a candidate for President- the four contender-Stephen Douglas, William Marcy, James Buchanan and Lewis Cass- deadlocked. On the 49th ballot the convention turned to a "dark horse" Franklin Pierce of New Hampshire. Pierce's views on slavery were not clearly articulated thus not offending anyone. His service as a General in the Mexican American War allowed the party to play the military hero card.
http://www.historycentral.com/elections/Conventions/1852DEM.html1868 Democratic Convention
New York, NY
July 4 to 9, 1868
Nominated:Horatio Seymour, of New York for President
Nominated: Francis P Blair of Missouri for Vice President
The Democratic convention of 1868 opened on the Fourth of July in New York City. Before the convention opened it was hoped that Supreme Court Chief Justice Samuel Chase would be the Democratic candidate, but keeping with his position he did not mount a campaign for the job. When the conventioned opened George Pendelton the 1864 candidate for Vice President was in the lead. President Johnson who had always been a Democrat and was not being renominated by the Republicans on whose ticket he had run in 1864 also sought reelection this time as a Democrat. After twenty two ballots in which no one acheived the required votes to win, a draft movement quickly developed to nominate the convention chairman Horatio Seymour. He was a supporter of Chase, but the momentum was too great and he was unanimously nominated to be the next President.
http://www.historycentral.com/elections/Conventions/1868DEM.html1920 Democratic Convention
Civic Auditorium San Francisco, California
June 28 to July 6, 1920
Nominated:James M Cox of Ohio for President
Nominated: Franklin D Roosevelt of New York for Vice President
The democrats opened their convention with no clear choice for President. President Wilson who was infirm was not going to run for another term. The convention looked at and rejected both Secreatary of the Treasury William McAdoo and Attorney General Mitchell Palmer. On the 44th ballot the convention turned to Governor James Fox of Ohio. Fox in turn selected Franklin D Roosevelt then Secreatry of the Navy and whose only elected office he had held had been State Senator as his running-mate.
http://www.historycentral.com/elections/Conventions/1920DEM.html