How to display the signup status of nodes in views templates?

I think you're looking for the "Signup: Status: Open/Closed" views field. Add that to your view, and then theme it however you want.

A) You realize that's potentially very inefficient, right? You're calling node_load() on every single node returned from your view. If you do that, you might as well make your view as trivial as possible and just have a nid field, instead of doing complicated JOINs to get other fields.

B) If you're doing a full node_load(), the signup status of a node is stored in $node->signup_status.

C) It might not be hurting anything, but I don't think you want this: $terms = array_keys($node->signup);

D) You never clear $classes, you just keep appending to it.

Something like this should be closer to what you need:

function garland_preprocess_views_view_unformatted(&$vars) {
  $view     = $vars['view'];
  $rows     = $vars['rows'];

  if ($view->base_table == 'node') {
    foreach ($view->result as $id => $item) {
      $node = node_load($item->nid);
      if (empty($node->signup_status)) {
        $class = " signup_disabled";
      }
      else {
        $class = " signup_enabled";
      }
      $vars['classes'][$id] .= $class;
    }
  }
}

However, the more efficient solution would be to include the field as I explained in #1, and then look at $item->whatever_it_is to see the value of this field, use that to append to the classes, and don't actually display the field itself. Getting that right is left as an exercise for the interested reader. I strongly recommend learning how to use a debugger or setting messages with the output of var_export() to figure out what's going on. devel.module can be very helpful, too.

Good luck,
-Derek

Are you talking about "signups enabled" (as in, this was at some point a signup-enabled node) or "signups open" (as in, users can currently sign up for this node)?

That wasn't clear. If you just want to see if signups are enabled on the node at all, you want this:

if (!empty($node->signup)) {
  $class = ' signup-enabled';
}
else {
  $class = ' signup-disabled';
}

I don't either. You must have a typo or something, since it's impossible my code would do that given what you're saying. Please debug this yourself. I've given you plenty of help.