Yes, a full range signal goes to the surround speakers. I am using PSB Image 5T towers for my surrounds, and running the surrounds full range. I really love hearing deep bass sounds coming from them in movies. There are a lot of scenes in which there is noticeable deep bass coming from behind my seating position on the sofa.
Now, that being said, since these speakers really start dropping off in their output around 80hz, you will achieve more overall deep bass and rumble by crossing them over at 60 to 80hz to a subwoofer. It just depends on what you like. Personally, I don't care for stomach churning deep bass levels, so that is why I am running them full range.
Of course, using towers allows you to experiment a bit and find out how you like it, while if you go with monitors, you will definitely not be running them full range and will probably cross them over at 80hz.