Yes he did. He made a statement to which the laws of logic pertain. In that sense, it is logical.
There is simply not enough information in that sentence to apply the laws of logic. That's why you have to start assuming, which makes the paradox.
That's just your opinion. A sentence doesn't have to be valuable to you or informative to you to qualify as logical.
A sentence does not have to be informative to qualify as grammatically sound, but that doesn't mean it qualifies as logical. If it did, applying logic to it would get you a logical outcome.
What if the man had said: "The following sentence is true. One plus one equals two". By your standards, would the first sentence be a logical proposition or not?
Without the second sentence it would not be a logical proposition. With the second sentence it would.
But if, as in curry's paradox, you were to put something like "one plus one equals six" into the second sentence, the logical proposition would be false.
You could assume
that the first part was true, in which case that would also validate the second part, but that would only be a repeat of what happened earlier. The validity of the sentence would no longer be decided by it's merits, but by an invalid axiom, which would be the cause of the paradox.