No, you cannot download courses to your console. All user-created courses in the TGC/PGA 2K series are housed on servers and require online connection to play.
TGCTours exists outside of 2K/HB Studios...they provide a 3rd-party location for scores to be displayed from their societies, and offer a place to keep track of courses they receive as submissions from designers. They don't actually have any courses on their website...all courses are stored in the 2K servers.