Does the alternator control all charging on a 1999 chrysler sebring convertible?

Yes, in a 1999 Chrysler Sebring convertible (and most cars), the alternator is the primary source of charging the battery. While there might be other minor sources of charging (like regenerative braking in some newer vehicles, which the 1999 Sebring certainly doesn't have), the alternator is responsible for almost all of the charging that keeps the battery topped up and powers the car's electrical system while the engine is running.