First online checker that I found:
The best I could do was test superman@ or batman@ but the results were meaningless.
Certainly, someone might enter in barack.obama@whitehouse.gov for fun. Presumably, emails to that address (and the official public email address, president@whitehouse.gov) get routed somewhere. But who is checking the emails sent to the president's public address? That likely requires a team of people, one of whom might have clicked on the link.