If you are talking about the input clip light, then no, you cannot damage an amp by overdriving the preamp, and with some amps (especially those with tube preamps) that can be a very nice sounding thing.
With most solid state amps, you would not want that clip light coming on much, not for safety reasons, but rather that it can sound like dog (i.e., solid state preamp clipping).
If, on the other hand, you are talking about your power amp/output clip light constantly coming on, that suggests, depending on the design of the indicator, that you are overdriving the power amp past its spec'd limits. Over time, that can cause some issues, and in a short time, you can blow a tweeter diaphragm pretty easily (the distortion coming out of the power amp is mostly very high frequency, which can damage tweeters that aren't protected.
Preamp clip light.... if it sounds good to you, have at it!