I'd think that it'd simply hinder their capability to function properly if at all, but I've been told that insufficient amperage can damage many devices. Do you have a particular reason for asking that question?
It might not damage it directly but if the power supply fails it might damage anything that's plug into it.
So lets say you power supply is 2 amps and device on it is 4, you'll overload the PSU. Usually it everything should just shut down but then if you power every thing on, many times, there could be damage.
Hope it helps.