The Supreme Court has never heard a § 793 case. Not even for American citizens. The constitutional problems with the Espionage Act are manifold, starting with the fact that it criminalizes speech. The notion that the government is going to successfully prosecute a case against a foreign national living on foreign soil for violating it seems far fetched.
Note also that to make this case, the government would have to claim "evil intent": either an intent to harm the United States, or an attempt to aid a foreign nation, or a reason to believe his actions would result in either. Assange may be no friend to the US national security apparatus, but he clearly seems to believe he's acting for the benefit of everyone, including the US. Check out US vs. Truong Dinh Hung (and the recent APAC case) for more detail; search for "scienter", the technical term for the requirement.
"Pentagon lawyers believe that online whistleblower group WikiLeaks acted illegally in disclosing thousands of classified Afghanistan war reports and other material, and federal prosecutors are exploring possible criminal charges, officials familiar with the matter said."
They haven't said what law WikiLeaks has broken, but it will be interesting to see what they come up with. The Espionage Act was the first thing that came to mind, but you may be right that it would be a difficult -- if not unconstitutional -- case.
