Shooting HD and converting to SD should give you better results than shooting SD on an HD camcorder, but how much better depends on your workflow and how you do the down-conversion.
You will get the best quality by capturing and editing as HD, and only doing the down-conversion at the end. Using a good resampling algorithm will help avoid aliasing artifacts such as stair-steps on diagonal lines, and twinkling/flickering of fine details and thin lines. It's a bit troublesome to use a separate re-sampling step though, so whether it's worth it depends on what quality you are trying to achieve.
Another possibility is to shoot HD and down-convert to SD during the capture process. The resampling is done by the camera, so the results are not the best. Then you can expect some further degradation during editing, depending on what filters and effects you use. The quality is not so good, however this option is probably the fastest one, because you would be editing DV format files which most PCs can do very easily.
Whether shooting HD and down-converting gives better results than using an SD camcorder in the first place depends on the 2 cameras you are comparing. For example, a Canon XL2 can produce superb SD images, and in my opinion, not many HD cams can achieve the same quality (for SD). There is also no resampling stage to introduce scaling artifacts. Others will disagree with me on this point though, so you need to be aware that it is not so simple to get a definitive question to this question. But in general, as long as the camera allows you to control the exposure as you want, the final quality will be up to the operator rather than which format you shoot.
