Check if select is displaying options

You can try listening on click, blur and key press event. I am just toggling a open variable to true or false on each of the event.

   // if menu is open then true, if closed then false
   // we start with false
   var open = false;
   // just a function to print out message
   function isOpen(){
       if(open)
          return "menu is open";
       else
          return "menu is closed";
   }
   // on each click toggle the "open" variable
   $("#myselect").on("click", function() {
         open = !open;
         console.log(isOpen());
   });
   // on each blur toggle the "open" variable
   // fire only if menu is already in "open" state
   $("#myselect").on("blur", function() {
         if(open){
            open = !open;
            console.log(isOpen());
         }
   });
   // on ESC key toggle the "open" variable only if menu is in "open" state
   $(document).keyup(function(e) {
       if (e.keyCode == 27) { 
         if(open){
            open = !open;
            console.log(isOpen());
         }
       }
   });
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<select id="myselect">
<option selected>Test 1</option>
<option>Test 2</option>
<option>Test 3</option>
</select>

You can use change event in case of not displayed, and focus event for displayed

$("#myselect").on({
  "change": function() {
    $(this).blur();
  },
  'focus': function() {
    console.log("displayed");
  },
  "blur": function() {
    console.log("not displayed");
  },
  "keyup": function(e) {
    if (e.keyCode == 27)
      console.log("displayed");
  }
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<select id="myselect">
  <option selected>Test 1</option>
  <option>Test 2</option>
  <option>Test 3</option>
</select>