There's no way they could continue to serve.

There's no way the Supreme Court would protect Trump's tax returns either. Federal Law grants the House the right to carry out investigations and do not protect the president from them.
It appears the Supreme Court has just changed the law where it applies to Trump. Apparently NO laws apply to the current president.

If Donald Trump takes a notion to stay in office there are simply no laws that can stop him. There are no courts that can stop him.

Donald Trump, his family, his friends, and his business are fully above the law.
Good coffee, good weed, and time on my hands...