Simply put, the answer is a resounding No. The function inside is defined but never called within the code block. As a result, it will not be executed and no value will be returned.

If you want to learn more about functions in JavaScript, you might consider exploring this resource: https://www.w3schools.com/js/js_function_definition.asp

It seems like there is an issue with the amount of code you have included here. Remember, on Stack Overflow it's best to provide a Minimal, Complete, and Verifiable example. To address your current situation without making significant changes to your code, one approach would be to switch your request to synchronous as previously advised and assign the result to a variable declared outside of the callback function. Here's a proposed solution:

function displayButton(){
    var result = false; // or true, depending on your default requirement
    //some code...
    //change to synchronous request!!

    var req = new XMLHttpRequest();
    req.open("GET", parent.Xrm.Page.context.getClientUrl() + "/api/data/v8.2/incidents(" + id + ")?$select=statecode", false);
    //...
    req.onreadystatechange = function () {
         if (this.readyState === 4) {
             req.onreadystatechange = null;
             if (this.status === 200) {
                  // skipping additional code for brevity
                  //...
                  //...
                  if (statecode_formatted == "Active") {
                        result = true;
                    }
                    else if (statecode_formatted == "Resolved")
                        result = false;
                    else {
                        result = false;
                  }
             }
         }
     };
     req.send();

     return result;       
}

To avoid modifying your entire code block due to its length, consider moving your calling function to a separate function with a callback mechanism. Within this callback, update the value of "result". The use of callbacks ensures that the function runs synchronously, allowing it to return the correct "result" value.

Your XMLHttpRequest is operating asynchronously in this scenario. Therefore, you won't be able to retrieve the response immediately, resulting in a delay in execution.

To address this issue, I implemented the following solution:

setTimeout(function () {

  },550);

You may want to try the following approach:

The modification I made was separating the XMLHttpRequest into a dedicated function called getResult(id), which is then invoked from the parent function displayButton().

Instead of directly returning a value from the child function, I store the boolean result in a global variable named boolValue.

In the parent function, before returning a value, I introduce a 550-millisecond delay to ensure that the asynchronous execution completes.

Below is the code snippet illustrating this implementation:

Parent function

var boolValue;

// Function triggered upon clicking a button in MS CRM.
function displayButton() {
    var Obj = parent.Xrm.Page.getAttribute("regardingobjectid");
    var ObjValue = Obj.getValue();

    if (ObjValue == null)
        return false;

    var EntityType = ObjValue[0].entityType;
    var Guid = ObjValue[0].id;
    var id = Guid.slice(1, -1);

    if (EntityType == "incident") {
        getResult(id);

        setTimeout(function () {
            if(boolValue == true || boolValue == false)
            {
                return boolValue;
            }
        }, 550);

    }
    else {
        return false;
    }


}

Child function

function getResult(id)
{
    var req = new XMLHttpRequest();
    req.open("GET", parent.Xrm.Page.context.getClientUrl() + "/api/data/v8.2/incidents(" + id + ")?$select=statecode", true);
    req.setRequestHeader("OData-MaxVersion", "4.0");
    req.setRequestHeader("OData-Version", "4.0");
    req.setRequestHeader("Accept", "application/json");
    req.setRequestHeader("Content-Type", "application/json; charset=utf-8");
    req.setRequestHeader("Prefer", "odata.include-annotations=\"*\"");

    req.onreadystatechange = function () {
        if (this.readyState === 4) {

            req.onreadystatechange = null;
            if (this.status === 200) {
                var result = JSON.parse(this.response);

                var statecode = result["statecode"];
                
                // Check if the selected case is active or resolved.
                var statecode_formatted = result["<a href="/cdn-cgi/l/email-protection" class="__cf_email__" data-cfemail="83f0f7e2f7e6e0ece7e6c3ccc7e2f7e2adc0eceeeef6edeaf7faadc7eaf0f3efe2fa_add56deeeaff9dfdea5eeebe4e5">[email protected]</a>"];
                if (statecode_formatted == "Active") {
                    boolValue = true;
                }
                else if (statecode_formatted == "Resolved")
                    boolValue = false;
                else {
                    boolValue = false;
                }
            }
            else {
                parent.Xrm.Utility.alertDialog("Zero");
            }
        }
    };
    req.send();
}

This methodology successfully resolved the issue for me.