A third-down conversion attempt occurs when a team runs a third-down play and either succeeds in getting the first down (or a touchdown), or fails and goes to fourth down.
The clock doesn't stop a play; if the clock runs to 0, the half ends when the play is over. So if the clock runs out before the third-down play begins, then no third-down attempt has occurred. If the clock runs to 0 while the third-down play is taking place, then it will count as an attempt, and it will be a successful attempt if it ends in a first down or a touchdown, and a failure if it does not.
One other thing to note about third-down efficiency statistics: If the first down is achieved as a result of a penalty, then it does not count as an attempt for statistics purposes.
The rules for determining third-down efficiency are defined in the NCAA Football Statisticians' Manual. From the 2013 Basic Interpretations section:
THIRD-DOWN EFFICIENCY — Third-down efficiency is the success a team has in converting third-down rushing or passing plays to first
downs or touchdowns. If a first down is obtained by penalty on a
third-down play or if a field goal is attempted on third down, the
offensive team is not charged with an attempt in determining