Do unused local variables in a method acquire memory in JVM?

Class level / Instance level variables will be initialized to their default values automatically. So, yes, they will occupy some space when a class is initialized / instance created respectively.

As far as method local variables are concerned, No, if they are just declared but not initialized, then they will not use any space, they are as good as ignored by the compiler..

If your code was this :

public static void main(String[] args) {
    int i;  // ignored
    int j = 5;
    String s = "abc";
    String sNull; // ignored
}

Byte code :

  LocalVariableTable:
        Start  Length  Slot  Name   Signature
            0       6     0  args   [Ljava/lang/String;
            2       4     2     j   I
            5       1     3     s   Ljava/lang/String;
   }