HAZMAT is a very big part of USAR.
Take a look at a standard building collapse. Hazmat comes in and will start looking into gas leaks, contents that might be a hazard within the building.
Here is an example of a 10-60 which had a hazmat issue
http://www.cbsnews.com/stories/2002/04/26/national/main507323.shtml
Also the other big thing hazmat will do is air monitoring at confined space incidents.
So no they don't carry ropes and things like that, but they are a very important part of the operations.