You can respond even later, as the code in delayed_2_example shows:

$httpd->reg_cb (
   '/test' => sub {
      my ($httpd, $req) = @_;

      $t = AnyEvent->timer (after => 2, cb => sub {
         my $txt = "CPU info:\n\n" . `cat /proc/cpuinfo`;
         $req->respond ([200, "ok", { 'Content-Type' => 'text/plain' }
+, $txt]);
      });
   },
);
[download]

So you can't "respond" until you have a meaningful content type, but that's OK as you can delay your response.