As with all electronic components, there can be issues with static discharge. When the PSU is not grounded, there are a few components that may not be able to handle the discharge. However, of all the components, I'd say the PSU is the most robust.
The answer there is an unequivocal "NO", you cannot damage any of the internals of a (properly built) PSU from external static - the chassis of the PSU is isolated from the electronics within (it could be dangerous otherwise)