Video is different from still pictures. Generally, the shutter on a still picture camera will be a lot faster.
Which high definition camcorder are you thinking about using? If the digital video is compressed a lot - like with the consumer-grade AVCHD hard disc drive or flash memory camcorders, they will pose a different set of issues because of the method and amount of compression applied to the video. These "issues" will be more pronounced when fast action is recorded.
If I set the shutter on my Sony HDR-HC1 or HDR-FX1 (both miniDV tape based HDV camcorders), to 1/500 second or 1/1000 second (or faster if the lighting is good enough), I can do a frame grab during editing and it will be fairly sharp. Typically, the default automatic shutter will set to 1/60 second or 1/125 second (depending on the lighting). Under fast action, a lot can happen in that time. The frame grabs will be blurred. Increasing the shutter speed reduces the amount of movement/blur because the time interval that light is allowed to hit the imaging chip is shortened.
I have successfully been able to run decent slow-motion playback and pull decent frame grabs from basketball video footage just by increasing the camcorders' shutter speed. That said, camcorders were designed for video (and audio) capture. They do that well. Anything else - or use of the video for anything else is an afterthought or work-around... or "convenience" feature. Camcorders typically do not do a good job at taking stills - whether by actually taking a still or by doing a frame grab. Still cameras were designed for still picture capture. They do that well.
If you want good video/audio, use a good video camcorder. If you want good stills, use a good DSC or DSLR.
I am trying to find out if its possible with an HD Video Camera to record something, then when you are replaying it, to pause it or something, and it allow you to take a "picture" of that freezed frame. I know a lot of video camera's double as a camera but I was curious if this also was a possibility.