watchable? Yes. Pristine? No.
Basically, the quality of the source video directly translates to how good things look on the display screen. SD quality video- especially most cell phone and cheap camcorder interlaced video- is NOT going to look as good as HD quality video (at least the HD that can max out what the

TV can handle: 720p30fps)
If it doesn't look very good on your 15" screen, it's not going to look very good on a 46" digital screen either. If your 46" happens to be an old Tube-type TV, SD and interlaced video will look better on it than a new DLP, LCD or Plasma of the same size & resolution.
But still, quality of the source = quality of the end result. We sometimes watch YouTube videos via

TV on my 65" 1080HDTV. But we are pretty much never impressed at the quality of the video... especially compared to say, DVD conversions or HD Camcorder movies we've shot ourselves.