There is no definite answer. There are no studies or available data on this. Any answers you get will be mostly based on assumptions and personal opinions, including mine, so take them with a pinch of salt.
Personally, I don't think that having a thick neck is necessarily an issue. It depends on how thick, though. I'm sure there is a point where it can become a problem, but I wouldn't automatically think that's the case for you. Well, I just said a bunch of nothing, didn't I? Sorry, I can't confidently say it'll work, because I don't know. But I can't say it won't work either, because it might also work well.
If I had to guess, I would say there shouldn't be an issue, because of the following reasons.
You can feel the pulse in your neck. This means there isn't a huge amount of fat tissue. The arteries are a little deeper and are at a little distance from the surface, so most people can only feel their pulse faintly. Also, most people cannot make themselves pass out by manually pressing on their neck; that is quite difficult to do. So what you feel isn't very different from what a thinner person would experience.
In hanging, the force on your neck will be far greater than what is normally required to block blood flow. In your case, the force on your neck will be about 60–120 kg, depending on whether you do partial or full suspension. Normally, only about 5–10 kg of force is required to compress the carotid arteries. Even if you don't have the ideal body type for hanging or these numbers are grossly inaccurate, there is still a huge margin of safety, and it should work.
Once again, I'm just speculating. YMMV.