I found a project that use a c328 camera to an arduino microcontroller (atmega328), take geo-tagged pictures continuously, and write them to an SD card. http://jarv.org/sdcam.shtml
Can I use the same or similar component to take the video?
Easy answer : No. Taking single frames and transferring them to external media is as much as an arduino can manage. (Its pretty good going it can manage that much considering its extremely limited resosurces).