Certainly if that works for you, that’s what I would suggest. On smaller screens, of course, some of the image will be cut off. If that’s a problem, you could make the image smaller and choose a background color for the body that the image merges into.
(I’m presuming the bg image is a picture of some sort. If it were just a colored background or gradient, it would be better to make a small slice of it and let it repeat across the screen.)
The few times I’ve used a graphical background image (i.e. a photo or artwork, not a gradient), I’ve just used a fixed-width design and said the hell with the whole issue. Of course, there’s no challenge to that…
One thing to be careful about is that you aren’t increasing the file size too much. A large image can increase the download time, and cause a noticeable lag in rendering, even with broadband.
If users have very wide screens, do you want the page to fill them? A good alternative is to set a max-width of maybe about 1200px, which will mean that (a) you don’t need to worry about making a background image larger than that, and (b) you can ensure that the design doesn’t become too stretched with very long lines if people have higher screen resolutions.