depends a bit on what modifications you did to your template, but something like this i would have thought
(choose whatever action hook in the template you need )

add_action('wppizza_loop_outside_end','my_custom_function',10,1);
function my_custom_function($query){
if(count($query->posts)<=0){
/**no items, do stuff**/	
}
/*or just use (probably better here)**/
if($query->post_count<=0){
/**no items, do stuff**/
}
}

PS: $query is an object with all sorts of things (i.e whatever the query returns) so if ->post or ->post_count is not what you need, maybe something else will do

still not sure exactly what you are after but let me guess a bit:

that page you are referring to seems to be just a list of subsites (i.e blogs) rather than menu items so I am not sure how the timed menu comes into play here ?!
or are you actually NOT using a multisite setup for this sort of thing ?
(or maybe I am just misunderstanding things)

in any case , thinking out loud and also writing a bit for anyone else that comes across this:

*if* you are using a multisite setup you would probably want to do/run a
switch_to_blog / restore_current_blog loop and within that do the following (of the top of my head, but should work). something like this:

if ( is_multisite() ) {
$blogs = $wpdb->get_results("SELECT blog_id FROM {$wpdb->blogs}", ARRAY_A);
if ($blogs) {
foreach($blogs as $blog) {
switch_to_blog($blog['blog_id']);
/*get wppizza options**/
$options=get_option('wppizza');
/*check if open**/
$isOpen=wpizza_are_we_open($options['opening_times_standard'],$options['opening_times_custom'],$options['times_closed_standard']);
if($isOpen){
/*do stuff if open**/
}else{
/*do stuff if closed**/	
}
restore_current_blog();
}}
}

(admittedly that wpizza_are_we_open function could be more user friendly , and i might just add another function that produces the same result without having to get the $options here seperately, but that’s for another day)

however, if the story is – as i suspect – you are *NOT* using a multisite setup and you are using the timed menu to open/close your individual shops by making pages unavailable – if every page refers to a restaurant/shop (as opposed to opening times per shop), then something like the following *might* be what you are looking for

/**************
get the timed menu options
**************/
$wpptmoptions=get_option('wppizza_timed_menu');
/**************
get all the menu items on a page (before timed menu settings have been taken into consideration) 
returns array with the keys being the page id and the values being the menu items
****************/
$wpptmMenuItemsOnPage=$wpptmoptions[items_on_pages];
/**************
get the timed menu settings
returns  array with the settings you have set in the timed menu (i.e dates/times/days/pages/menuitems etc
**************/
$wpptmSettings=$wpptmoptions[timed_items];

so, assuming you are just excluding whole pages (as a page would be all items for a restaurant here if i interpret things correctly)
something like this (there are probably other ways to code this too, but as a dummy example)

$wpptmCurrentTime=current_time('timestamp');/*wordpress time*/
$shopOpen=array();
foreach($wpptmSettings as $tm){
if($tm[enabled]){
/*
check here if $wpptmCurrentTime is within set time date etc
probably want to convert the below to timestamps to compare to $wpptmCurrentTime
returns stuff like
$tm[start_date] => 2014-12-02//set start date
$tm[end_date] => 2014-12-25//set end date
$tm[start_time] => 08:45//set start tim
$tm[end_time] => 17:45	//set end time
$tm[day]=>Array([1] => 1,[2] => 2) //returns array of set days 0 to 6 
$tm[enabled] =>1
etc
*/
if(time-date-check-passed[you'd need to write this check]]){
$shopOpen=array_merge($shopOpen,array_keys($tm['pages']));
}
}}
/**flip keys to be able to use isset as opposed to in_array (and also end up with unique keys)**/
$shopOpen=array_flip($shopOpen));

/**within your pages loop you could now do smth like**/
if(isset($shopOpen[$pageId])){
/**do stuff if open**/
}else{
/**do stuff if closed**/	
}

`

instead of the “wpizza_are_we_open” function referred to previously , you should now (as of v2.11.5.10) simply be able to use

wpizzaShopOpen();

without any arguments and omit

$options=get_option('wppizza');

there