Checking Internet inside a Coroutine

I am attempting to check the internet connection at multiple points during the actual gameplay without bombing the fps of the game. I thought I could achieve this through coroutines but at the moment when I call StartCoroutine(CheckInternetCoroutine()) it seems to run the entire CheckInternet()in one frame causing the game to lag a full second or more even with a fast internet connection.

Am I using the Coroutine incorrectly? Or can CheckInternet()simply not be broken down into a Coroutine in the manner in which I have presented, if so how do can I do that?

StartCoroutine(CheckInternetCoroutine())is called after a certain gameobject has been instantiated.

 IEnumerator CheckInternetCoroutine(GameObject CloneObject, Vector3 loadedSpawnPos) {
 
             internetChecker.CheckInternet ();
             CloneObject.transform.position = loadedSpawnPos;
             yield return null;
 }

Then within the class InternetChecker:

 public void CheckInternet() {
         if (TestInternet() != "We are connected to the Internet") {
                 MenuManager.PauseGame ();
                 noInternetCanvas.SetActive (true);
                 StartCoroutine (PauseBeforeCheckingConnectionAgain); 
             } else {
                 noInternetCanvas.SetActive (false);
                 MenuManager.ResumeGame ();
             }
     }

 public string TestInternet(string testSite = "http://google.com", string testHtmlString = "schema.org/WebPage") {
         Debug.Log ("Testing internet at " + Time.realtimeSinceStartup.ToString());
         string htmlText = GetHtmlFromURL (testSite);
         if (htmlText == "No connection") {
             return "No connection";
         } else if (!htmlText.Contains (testHtmlString)) {");
             return CheckInternetRedirectedLink ();
         } else {
             Debug.Log ("We are connected to the Internet from TestInternet at "  + Time.realtimeSinceStartup.ToString());
             return "We are connected to the Internet";
         }
     }
 
     public string GetHtmlFromURL(string resource) {
         string html = string.Empty;
         HttpWebRequest webRequest = (HttpWebRequest)WebRequest.Create (resource);
         try {
             using (HttpWebResponse webResponse = (HttpWebResponse)webRequest.GetResponse()) {
 
                 bool isSuccess = (int)webResponse.StatusCode < 299 && (int)webResponse.StatusCode >= 200;
                 if (isSuccess) {
                     
                     using (StreamReader reader = new StreamReader(webResponse.GetResponseStream())){
                         char[] chars = new char[80];
                         reader.Read(chars,0, chars.Length);
                         foreach(char ch in chars) {
                             html += ch;
                         }
                     }
                 }
 
             }
         }
             catch {
                 return "No connection";
                 }
         return html;
     }

Any help would be appreciated, thank you!