Check out LWP/Protocol/http.pm
  When request is called here, your coderef is in $arg

sub request {
  my($self, $request, $proxy, $arg, $size, $timeout) = @_;
 ...
    my $content_ref = $request->content_ref;
    $content_ref = $$content_ref if ref($$content_ref);
....
        if (ref($content_ref) eq 'CODE') {
            my $buf = &$content_ref();
...

http.pm doesn't look at $arg as a code ref.
Instead it looks at $content_ref.
But if $content_ref was a code ref, then you'll get a run time error.

It'll never work !  This feature is totally broken.