as far as i know , no. Once you awaken their skills , they pretty much get a new skill. Which is why some people recomanded having 2 of some units (most notably anya) , since their normal skill and AW skill makes them into 2 different units.
For example normal skill anya is a high end tank. AW skill anya is a dps unit (SAW doubles her damage , and she attacks everything in a 120 range around her)