In theory, there's no reason why not. It is, after all, just a TV, albeit a large one. The big issue is likely to be the response time of the TV if you're a serious gamer - there are huge differences (~5msec - 200+msec) between TVs that can cause unacceptable lag. That's nothing to do with screen size, though. Your 770 should have no trouble driving it at maximum resolution: it's not screen size that's important, it's the number of pixels, and that doesn't vary from a full HD 32" TV to a full HD 60" TV. Connecting it is unlikely to be an issue: I assume both the card and the TV support HDMI. The only thing to watch out for is how close you are to the TV: with a 47" screen, unless you sit a reasonable distance back, the pixels will be plainly visible and will spoil your enjoyment.
I may not have answered your question. Why do you think it might not work?