No, they're a government agency pretty much all the way since they're governed directly by Congress. This entire weekend off proposal isn't going to happen unless Congress approves it.
Actually, while Congress normally mandates Saturday delivery, they forgot to mandate it in the continuing resolution/Fiscal Cliff deal. Because they forgot, the Postal Service is taking advantage of this. The whole thing is basically a political showdown with Congress. Daring them to affirmatively legislate something that will lose the Post Office money. The real target is the pension requirement, which will make them self-sufficient once again, but who knows with Congress.