Valid, but worthless syntax in switch-case?

Perhaps not the most useful, but not completely worthless. You may use it to declare a local variable available within switch scope.

switch (foo)
{
    int i;
case 0:
    i = 0;
    //....
case 1:
    i = 1;
    //....
}

The standard has the following sample:

EXAMPLE    In the artificial program fragment

switch (expr)
{
    int i = 4;
    f(i);
case 0:
    i = 17;
    /* falls through into default code */
default:
    printf("%d\n", i);
}

the object whose identifier is i exists with automatic storage duration (within the block) but is never initialized, and thus if the controlling expression has a nonzero value, the call to the printf function will access an indeterminate value. Similarly, the call to the function f cannot be reached.

P.S. BTW, the sample is not valid C++ code. Clang complains about jump to default: (and to case 1:):

error: cannot jump from switch statement to this case label
default:
note: jump bypasses variable initialization
int i = 4;

However just defining i without initialization compiles.

Does this serve any purpose at all?

Yes. If instead of a statement, you put a declaration before the first label, this can make perfect sense:

switch (a) {
  int i;
case 0:
  i = f(); g(); h(i);
  break;
case 1:
  i = g(); f(); h(i);
  break;
}

The rules for declarations and statements are shared for blocks in general, so it's the same rule that allows that that also allows statements there.

Worth mentioning as well is also that if the first statement is a loop construct, case labels may appear in the loop body:

switch (i) {
  for (;;) {
    f();
  case 1:
    g();
  case 2:
    if (h()) break;
  }
}

Please don't write code like this if there is a more readable way of writing it, but it's perfectly valid, and the f() call is reachable.

Assuming you are using gcc on linux, it would have given you warning if you're using 4.4 or earlier version.

-Wunreachable-code option was removed in gcc 4.4 onward. https://gcc.gnu.org/ml/gcc-help/2011-05/msg00360.html

You got your answer related to the required gcc option -Wswitch-unreachable to generate the warning, this answer is to elaborate on the usability / worthyness part.

Quoting straight out of C11, chapter §6.8.4.2, (emphasis mine)

switch (expr)
{
int i = 4;
f(i);
case 0:
i = 17;
/* falls through into default code */
default:
printf("%d\n", i);
}

the object whose identifier is i exists with automatic storage duration (within the block) but is never initialized, and thus if the controlling expression has a nonzero value, the call to the printf function will access an indeterminate value. Similarly, the call to the function f cannot be reached.

Which is very self-explanatory. You can use this to define a locally scoped variable which is available only within the switch statement scope.

Not only for variable declaration but advanced jumping as well. You can utilize it well if and only if you're not prone to spaghetti code.

int main()
{
    int i = 1;
    switch(i)
    {
        nocase:
        printf("no case\n");

        case 0: printf("0\n"); break;
        case 1: printf("1\n"); goto nocase;
    }
    return 0;
}

Prints

1
no case
0 /* Notice how "0" prints even though i = 1 */

It should be noted that switch-case is one of the fastest control flow clauses. So it must be very flexible to the programmer, which sometimes involves cases like this.

It should be noted, that there are no structural restrictions on the code within the switch statement, or on where the case *: labels are placed within this code. This makes programming tricks like duff's devise possible, one possible implementation of which looks like this:

int n = ...;
int iterations = n/8;
switch(n%8) {
    while(iterations--) {
        sum += *ptr++;
        case 7: sum += *ptr++;
        case 6: sum += *ptr++;
        case 5: sum += *ptr++;
        case 4: sum += *ptr++;
        case 3: sum += *ptr++;
        case 2: sum += *ptr++;
        case 1: sum += *ptr++;
        case 0:
    }
}

You see, the code between the switch(n%8) { and the case 7: label is definitely reachable...

It is possible to implement a "loop and a half" with it, although it might not be the best way to do it:

char password[100];
switch(0) do
{
  printf("Invalid password, try again.\n");
default:
  read_password(password, sizeof(password));
} while (!is_valid_password(password));