No, they cannot impeach a president for taking the nation to war without congressional approval. The president has that authority. Korea and Viet Nam are shining examples of that authority. There was no WPA back then, yet the president deployed troops anyway.
Again, the WPA was not some kind of way for congress to bypass the process of declaring war. Its intent was to curb the authority of the president over military deployments. So far presidents have, at least minimally, gone along with the requirements of WPA. But, constitutionally, they are not required to, and it would not be a crime or any other type of impeachable offense if some future president, who sees a need for military action that congress won't approve of, tells congress to take WPA and shove it.