It does. You can even try it out yourself. Install Ungoogled Chromium, go to google.com and paste the following code in the Developer console (which you can bring up by pressing F12 and clicking on 'Console' at the top of the DevTools interface):

    chrome.runtime.sendMessage(
      "nkeimhogjdpnpccoofpliimaahmaaome",
      { method: "cpu.getInfo" },
      (response) => {
        console.log(JSON.stringify(response, null, 2));
      },
    );

If it returns nothing or an error, you're good. If it returns something like this:

{
  "value": {
    "archName": "arm64",
    "features": [],
    "modelName": "Apple M2 Max",
    "numOfProcessors": 12,
    "processors": [
      {
        "usage": {
          "idle": 26890137,
          "kernel": 5271531,
          "total": 42525857,
          "user": 10364189
        }
      }, ...

it means that the hidden extension is present, and *.google.com sites have special access in your browser.