Yes, you can damage headphones when using an underpowered amp, but the chances of doing so are probably very unlikely.
Clipping is when an amplifier is pushed to its maximum. The amplifier is being sent a signal which is beyonds its output capabilities, and the signal gets clipped off. When this happens, the amp puts out pure DC power, which can overheat the voice coils. (There are other causes of clipping too, but I'll keep things simple).
Really, any damage is much more likely to happen with higher power amps that are overdriven, because they would put out higher DC current which would overheat the drivers more quickly. Of course, you can also damage the headphones by simply playing them too loud with an amp that can handle the load.
Clipping can be identified by clicking like noises, mostly notable in the midrange and treble.
Most PCDPs with cheap, underpowered amps can clip very easily, even at mediocre listening levels. Damage from this isn't likely.