I was wondering if it is possible to plug up my main 27" monitor, and then put a HDMI cable on my video card to my T.V. (for movies) without frying the video card.
Like, for example, if the T.V. is NOT in HDMI mode, will it tax the video card at all?
You'll be fine. Yes, the card will be working just slightly harder if either display acts like an extended display. If you are cloning the desktop on both displays, then there shouldn't be any additional minor stress.