You do need a letter, there is a good chance they may not give it to you. I know people who have been turned down. They have no way of recovering the vehicle if you default. You may have to pay off the loan or put up a bond in the amount owing for the time its in Mexico. If there nothing on the registration indicating it is financed and the registration is in your name it can be a case of don't ask don't tell.
In your case, going to Baja you won't need a permit for the vehicle anyway, so you can get away with it.
It is because of this I never got a car loan, I used the line of credit against my house. No vehicle lien.