How to connect popup script to content script on chrome internal browser pages?

Question

I'm trying to send a message to the content script running on the page in the active tab. This works fine for any normal page. However, when I try to do this for pages starting with chrome:// in the URL I get an error:

Unchecked runtime.lastError: Could not establish connection. Receiving end does not exist.

This is the code I'm trying to run:

// popup.js
window.addEventListener('load', (event) => {
    // In case the next line yields chrome://new-tab-page
    // or chrome://extensions for example
    chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
        // Request data from app
        chrome.tabs.sendMessage(tabs[0].id, "siteData", function(response) {
            // error!
            // Log app's response
        }
    }
}

//content script (even though it doesn't reach the content script)
// Site Data request
chrome.runtime.onMessage.addListener(
    function(request, sender, sendResponse) {
        if (request === "siteData") {
            sendResponse({siteList: siteList, site: site, hostname: hostname});
        }
    }
);

Is it possible at all to establish a connection with a content script on an internal chrome page? Does the internal page even execute the content script?

Thank you

Edit: This Can you access chrome:// pages from an extension? answered my question.