This is a tower function, so someone from there would be better to answer.

TRACON perspective -- go arounds mean more work for us, and we don't like them. Personally, I say do whatever you think is prudent in the situation. If I'm working and you come back to me, I will attempt to put you as close to the front of the sequence as possible (I think most controllers here will). I can't speak for everyone, though.

Bottom line -- if you land without a clearance and nothing happens, it's probably no big deal. If you land without a clearance and something bad happens, you and I both are in trouble (you might be dead, my life might be changed forever because of your death).

If you're on final, the tower knows about you whether they talk to you or not. Most controllers will assume you're just going to land if they don't talk to you -- maybe your radio broke: in that case, it's probably safer for you to be on the ground than flying around Chicago airspace not talking to anyone, even if you didn't hear the magic words "cleared to land".

Let's say it is 200' overcast and 1sm visibility, you check in at TAFFS and no one answers and you don't hear another transmission to anyone all the way to the runway. Do you go missed, follow the published missed, hoping ATC cleared a path for you, then try to go shoot an approach somewhere on your own, or do you land and hope ATC ensures the runway is clear? As a controller, I'm going to assume you are landing and do everything humanly possible to make sure the runway is clear.

But, you're ultimately the pilot in command, and we will accommodate you to the best of our ability whether your land or go around.