If you are charged with vehecular homicide in TN and licensed in Alabama does TN report it

Vehicular homicide is a criminal offense, not a motor vehicle offense, so I don't know if it's reported between the motor vehicle agencies.  But the arrest and the outstanding charge, if you're waiting for trial, or the verdict against you if it's been entered, are on the national criminal reporting system, and Alabama, of course, has access to that.

I'd think that if you're facing something like this, your driving privileges wouldn't be near the top of your worry list.  You need a lawyer, if you don't already have one.