Of course, they do. Some countries even designate incels as terrorists, as ridiculous as that sounds (because it is). Once you designate a group as terrorists, the spy agencies are tasked to spy on you as part of their mandates. If you become a POI (person of interest), then everything you do is monitored (online activity, phone calls, SMS, banking activity, and even your physical activity i.e., your routines, what you do, and which circles you're in).
Like @Ehwhatever said, much of it is using AI, which is used to filter out keywords, phrases, and posting patterns. If the parameters are met, it triggers a hit, then a human looks into it to determine whether or there's a potential threat. If the user is deemed a potential threat (POI), then all of the shit I mentioned above takes place. In addition to that, there are also glowies on the forum (but they're mostly passive and lurk). The active ones are usually provocateurs who bait and encourage you to incriminate yourself, or at the least to open up and reveal something honest about yourself (your moral and political views, for example) in order to profile you.