I'd like to use time-lapse option on my HC-1 or Sony still camera of sunrise/sunset. Might the brightness of the sun damage the image sensor (CMOS in the HC-1, CCD in the still camera)?
It is a concern and i certainly can't recommend it. On the other hand, i've done exactly this with a "throw-away" camcorder, recorded about 15 sunsets with the lens pointed right at the sun for 60 to 100 minutes each time. It hasn't done any damage at all. But that's just my experience; i'm not recommending that it's ok for you do to with your camera.
I wouldn't recommend it either. However, I have a CCD security camera that has been in service 24/7 since 1993. It points due east and on clear days, the sun comes up over the horizon and shines straight into it for almost two hours. There is absolutely zero sign of damage after fifteen years. However, that camera cost $250. I would be somewhat reluctant to take my $3,000 camera and do the same thing.
Might want to use auto exposure with the right aperture and shutter speed available as a safeguard. Do a test at the brightest part of the day and see if you have a setting that the camera accepts. Much better to be there with camera monitoring. Any major overexposure for a long time is likely to do some damage. For starters the CDD could get very hot - you are focusing the sun on it! Get the right ND or smoke screen in the matte box before you ever try this.