What happens if I update an app using its built-in ability that I built/installed through MacPorts?
Probably not as Macports keeps information about what versions are installed etc in a database /opt/local/var/macports/registry/registry.db So when a new version comes out from Macports it will compare with this db.

However if you have done an update otherwise then why do you want macports to update it as the versions won't be as expected.