No. Construction material and debris (dirt, concrete and rocks) will not be picked up by the garbage company. These items will need to be disposed of either by renting a dumpster from Republic Services (972-225-4207 or 972-225-5252) during renovations or hauling it to Skyline Landfill located at 1201 N Central, Ferris, Texas 75125.
I guess, you have to contact sanitary and waste department from your local community if they are handling the same concern. But first I suggest that you have that items for disposals segregated from their corresponding form. You can also salvage items that still holds values and have them for sale to those who cares recycling materials. Like me that I am into it, in fact I am inspired from this door and installation store http://caldwells.com/interior-doors/shaker-doors, their idea thought me some positive things about waste and usable disposing.