there is no genlock - in computer video world- you have to really remember vga and dvi are not video signals as per the world of sdi and hdsdi- VGA and DVI clock rates have nothing to do with sdi clock rates-
nothing is synchronised together- everything is frame buffered - genlock comes from a technological era when nothing was frame buffered - and mixers had to work with the video signal without being able to store it.
projectors generally do completely their own thing - they arent locked to anything - except the technology inside them which follows its own rules- with DLP its the DLP rates.