The building is not prominent in any missions. It is simply there as a cathedral based on St. Patrick's Cathedral. In the grounds of the cathedral, however, there is a garden, where there are usually people walking around or sitting on the benches.
The stained glass windows on the Columbus Cathedral have a design exactly the same as the Triforce in the Legend of Zelda games.
In GTA IV if the player goes on a helicopter ride with Brucie Kibbutz, the Cathedral is one of the locations Brucie will request to ride to.