Yes it is possible. I use the following function to email me on user_meta updates while I am debugging my custom site at https://www.thelightningpath.com/
You have to play with this otherwise you could get a lot of actions, but this is the basic template.
add_action('updated_user_meta','log_user_action',10,4);
function log_user_action($meta_id='', $object_id='',$meta_key='', $meta_value='') {
global $current_user;
if ($meta_value=='' || $meta_key =="last_viewed_8")
return true;
$message = sprintf("Changing <b>User,/b> %s <b>meta key</b>: %s <b>value:</b> %s",
$current_user->user_nicename,
$meta_key,
$meta_value);
wp_mail('[email protected]', "Changed meta data for user", $message);
}