Can websites detect use of simple Tampermonkey scripts?

Out of curiosity and not being able to find a clear answer, I was wondering. Are websites able to detect use of Tampermonkey user-scripts? If so, is it any script or only if it has specific functionalities? Would a simple script like the following be detectable by a website?

(function() {
  var randomizer = Math.floor(Math.random() * 241) + 20; //Gets a random number between 0 and 240, then adds 20
  //console.log(randomizer);
  setTimeout(function(){ location.reload(); }, randomizer*1000); 
})();

Solution

tl;dr - no

The browser, nor the Tampermonkey plugin do not advertise the presence of userscripts. That is there isn't a straightforward way to just write if(tampermonkeyActive) and detect it.

However, webpage may implement anti-tampering techniques. These may not be directed at Tampermonkey, but any type of suspicious behaviour. This may include:

Suspicious amount of activity per unit of time per user
Activity when the webpage is not in focus
Unexpected global variables or function calls
Checking isTrusted on events.

Of all these, I have only experienced the first example, that is logging activity server-side and manually reviewing it. Thus if you're trying to automate something and the site owner is not keen on it, you should consider making it look human-like.

Security

Tampermonkey script already runs in wrapped scope, so the self-invoking function is redundant.

Detecting a userscript can be something a malicious actor might want to do. If you use @grant to get any of the special features of tampermonkey, and also use @grant unsafeWindow, leaking any of the functions could allow actor that detects that to hack your browser. It would take a lot of effort though - they need to detect the userscript, then manually hack it, since every userscript is different.