Does subduction of continental crust happen at continental-continental convergent boundaries?
Both of the processes you describe occur; in some cases such as the Himalayas the plates are not subducted and a moving plate, in this case the Indian plate, bulldozes the continental crust ahead of it into a high mountain range. In most cases, such as the Pacific rim for example, subduction is the norm. Where there is subduction there are usually many volcanoes, and this is certainly the case on the Pacific rim. The subducted crust carries rock and water down into the hot mantle, where the friction,heat and water content tend to liquefy it,and it rises to the surface to form volcanoes. To answer your specific question, no. there is no subduction when continental crust meets continental crust, as is the case with the Indian plate meeting the Eurasian plate. Subduction occurs when sea floor spreading forces a plate underneath the lighter and more buoyant continental crust.