Chrome Version       : Version 71.0.3563.0 (Developer Build) (64-bit)
URLs (if applicable) :
Other browsers tested:

Using the script at the end of the page I see that `headless: false` causes Chrome to disconnect from the proxy at `page.setOfflineMode(true)`, while Chrome remains connected to the proxy if `headless: true`. The relevancy of this inconsistency is due to automatic IP address rotation whenever a new connection is established toward the proxy.

The script can run as-is; a valid proxy argument is required.

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const puppeteer  = require("puppeteer");

let browser, page;

async function openBrowser() {
    browser = await puppeteer.launch({
        args:            [ `--proxy-server=http://localhost:${proxyPort}` ],
        headless:        false,
        defaultViewport: { width: 1024, height: 768 }
    });
}

async function openPage() {
    page = await browser.newPage();
    await page.setUserAgent("Mozilla/5.0 (X11; Linux i686; rv:59.0) Gecko/20100101 Firefox/59.0");
    await page.setDefaultNavigationTimeout(latencyMs);
    await page.setExtraHTTPHeaders({'Accept-Language': 'en-GB,en-US;q=0.9,en;q=0.8'});
}

async function checkAddress(page) {
    let pageText = "",
        url      = "http://whatismyip.akamai.com/";

    await page.goto(url, { waitUntil: "load" });
 
    pageText = await page.evaluate(() => document.body.innerText);
    console.log(pageText);
}

await openBrowser();

while (true) {
    await openPage();
    await checkAddress(page);
    await page.setOfflineMode(true);
    await page.setOfflineMode(false);
    await page.close();
}