you can connect as many displays as you like to your computer assuming you have enough outputs.
with six outputs you could have 6 displays.
if you want to have the card attached to a TV in the lounge for when you're awake and a TV in the bedroom for when you're in bed that you want to display the same content then you're better of trying to split the signal with a video splitter rathe than getting 6 video out graphics headers.
if you want to be able to both watch and record at the same time this is also possible, but you'll most likely experiance quite a jumpy playback and a possibly rubbish recording as you'll find these two opperations are both disc intensive, so they'll eat your RAM up with caching as well.
in this instance you'll probably more likely want a box to record and a box to watch on...
if you don't want multiple PC boxes lying around then you could always invest in an external media player drive.