Impersonating a federal officer or employee is a crime. 18 U.S. Code § 912

(technically you have to obtain a document, money, or other thing of value to run afoul of that particular law, but getting a reply to a successful spoof might qualify, and who knows whatever other laws it might violate, 25 CFR § 11.432 perhaps).

Oh noes! And we all know how famously rigorously spam and phishing is prosecuted!

(I didn’t actually do that. What stopped me is no longer being 12 years old, not a fear of going to Gitmo for sending an obviously fake email.)