This is a flat, substabtial interface with the 10th Amendment’s allowance of states to manage and run elections. If a state allows elections such that they aren’t denied on account of race, gender, and people under 18, they can be run however the states deem. Requiring someone to register with the federal government is not a power of Congress
It’d be quite a circus too since election interference is a state crime, so he’d be carted around for trial in every state that charged him (basically every blue state, since the red state governments are full of people who probably waived the tiki torches).