Did that already; no joy. It's not a problem because of the overscan slider in OSX, but it was a huge annoyance before I upgraded the mini (you need the built-in HDMI to get the overscan adjustment).
Unfortunately you're most likely losing resolution in this case. If, for example, your TV is cutting off 3% of the image, then the video card is scaling your whole desktop down from 1920x1080 to ~1862x1048, which will result in more than 3% apparent resolution lost due to less-than-optimal interpolation.