A more useful answer is: I did this once, many years ago. Back then it was a matter of hooking up PhantomJS and making sure your user string was set correctly. Since PhantomJS was – I think – essentially the same as what headless chrome is today, the server can't determine that you're running a headless browser.
Now, it's not so easy nowadays to do that. There are mechanisms to detect whether the client is in headless mode. But most websites don't implement advanced detection and countermeasures. And in the ideal case, you can't really detect that someone is doing automated scraping. Imagine a VM that's literally running chrome, and the script is set up to interact with the VM using nothing but mouse movements and keyboard presses. You could even throw in some AI to the mix: record some real mouse movements and keyboard presses over time, then hook up some AI to your script such that it generates movements and keyboard presses that are impossible to distinguish from real human inputs. Such a system would be almost impossible to differentiate vs your real users.
The other piece of the puzzle is user accounts. You often have to have "aged" user accounts. For example, if you tried to scrape LinkedIn using your own account, it wouldn't matter if you were using 500 IPs. They would probably notice.
It's hard to counter a determined scraper.