No. A signing statement can't nullify an Act of Congress.
A law that contains mutually cancelling parts is interesting, but it opens up the great possibility that the Courts will make the final call based on the legislative history (what there is of it in this case).
And a bill that says, "Do X" and then says, "Don't do X", is often looked at as intending to Do X.
So it would likely favor the Rats either way.