Though Steve Thomas doesn't speculate in his book that Patsy wrote the note to fool John, Thomas does say that John must have recognized his wife's writing mannerisms all over it. There are elements of the note that relate to John and which he acknowledged: a reference to his Atlanta Fat Cats club, his net 1996 bonus. There are things he was probably not aware of for some time, to wit, the S.B.T.C. sign-off from the open Bible on the desk in his third-floor study.
There are words taken from the Tom Clancy books John liked to read. In '98 the police asked Patsy if she read Tom Clancy. (The transcript spells it "Clancey.")
So my conclusion is that Patsy didn't write the note to fool John--or even the police in the long term. She wrote the note to implicate John.