If it is operating properly, a protein skimmer will remove any hydrophobic molecules from the water. It will not remove hydrophillic compounds. Some proteins are hydrophobic, some hydrophillic. Some contaminants and trace elements are hydrophobic, some are not...
A protein skimmer will remove some trace elements, they are still one of the favored filter of hobbyists. The good does out way the bad in most cases.
Personally, I no longer use one, have not for 3 years on any of my tanks.