Does the implicit narrowing conversion work with the method return statement?

Yes, the implicit narrowing conversion work with the method return statement. For example,

class Program {
   byte method_1() {
       return 126;
   }
   byte method_2() {
       final int m = 127;
       return m;
   }
   byte method_3() {
       final int m=128;
       return m;   //compile time error because m is not in the range value (-128 to 127) of byte
   }
}

14.17 The return Statement in JLS 3.0: 

A return statement with an Expression must be contained in a method declaration that is declared to return a value (8.4) or a compile-time error occurs. The Expression must denote a variable or value of some type T, or a compile-time error occurs. The type T must be assignable (5.2) to the declared result type of the method, or a compile-time error occurs.

"The type T must be assignable (5.2) to the declared result type of the method, or a compile-time error occurs" indicates that the implicit narrowing of integer constants is allowed in the method return context.