Isn't the idea that they can decide whether it's a user or a bot based on what the user does in general, not just whether their browser executes JS on this page that you want to protect?
Running headless chrome is trivial, so just having it sit on the one page where you need to check it won't help much. Collecting more data on the user's action on your site will provide a much clearer picture, much like a video from somebody walking through a store will help you make a decision about whether he's trying to steal something than a single picture of him standing at the check out.
The big "if" here is whether or not Google is actually factoring the user's activity into the score. For all we know, there could be a 80/20 split between "Google account activity" and "human-like behavior on website" when Google outputs a trust score.
Running headless chrome is trivial, so just having it sit on the one page where you need to check it won't help much. Collecting more data on the user's action on your site will provide a much clearer picture, much like a video from somebody walking through a store will help you make a decision about whether he's trying to steal something than a single picture of him standing at the check out.