yes, depending on the amp. There is extra power. The power supply will be strained. Various power semiconductors may become damaged as well, though this mod of operation can be better for some amplifiers.
amplifiers are designed to handel clipping, as it is deceptively difficult to ensure you won't clip the amplifier, due to the way filters and processors can align frequencies to produce peaks that are greater than full scale.
Minor clipping is nothing to worry about, and provides benefits to most "street" users in that it increases average SPL by reducing dynamic range. music is now louder on average. This also allows multiple tracks, recorded at different volumes, to seem nearly equally loud.
of course, at moderate levels, the tonality and the transient characteristics of the music may be degraded as described above.
At severe levels, the amplifier and attached speakers may become damaged. tweeters now receive extra power (the distortion contains high frequency content), and the tweeters may become damaged. woofers and other speakers may be damaged as well.
(also note that amp gains are best listed relative to rated output, not knob rotation. basically, the amp could attain full power output with either a high gain setting and low signal, or a high signal and low gain. because there are a wide range of HU outputs and amp inputs, percentages of knob rotation are not overly useful)