Definitely not, or else every sensor in a DSLR would have been damaged as soon as someone tried to clean it. Maybe - just maybe - you could damage it if you took a huge telephoto, focused on the sun and then left it open for minutes at a time, but that would be due to the same reason that doing the same thing to a piece of paper would ignite and burn it. (In the case of the sensor you'd probably just be melting it.) But you really have to try hard to do that. As noted, for most of us when we clean the sensor we are leaving the shutter open for minutes at a time in a relatively bright environment and the resultant frame is 100% blown, with no damage. Some folks even use a tool - Artic Butterfly? - that illuminates the sensor for cleaning.
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!