For this to apply to election to president, it would mean Congress can add additional requirements to those in the Constitution. I doubt this would be Constitutional.
In fact, I doubt it applies to election to any federal office. Such are not "employees" in the strict sense of the term.
http://www.sss.gov/FSbenefits.htm
FEDERAL JOBS
A man must be registered to be eligible for jobs in the Executive Branch of the Federal government and the U.S. Postal Service. Proof of registration is required only for men born after December 31, 1959.