In General, for live streams you can't, no. There may be some add-ons that enable this functionality, but I've only seen downloads of completed media files (TV shows/films/DVD rips) via apps and add-ons, rather than live streams.
For downloading videos, Google the name of your favourite add-on or app, and see if there is a download facility, and if so whether you can change the default save location. If you can't, don't forget to move the video from internal storage to a memory card/USB device afterwards.