Here is the text from The Adventures of Pinocchio where the fairy tells him why his nose is growing:
The Fairy sat looking at him and laughing.
"Why do you laugh?" the Marionette asked her,
worried now at the sight of his growing nose.
"I am laughing at your lies."
"How do you know I am lying?"
"Lies, my boy, are known in a moment. There are two
kinds of lies, lies with short legs and lies with long noses.
Yours, just now, happen to have long noses."
The Oxford dictionary defines a lie as:
an intentionally false statement.
Merriam Webster's definition of a lie is:
to make an untrue statement with intent to deceive
While we can't verify that the author went by these particular definitions, the meaning of "lies" can be presumed to be equivalent to the above definitions. The defining factor of a lie that separates it from a mere false statement is that there is an intent to falsify something.
I doubt we will ever find a canonical instance where Pinocchio states a false statement (without an intention to deceive) just to test if his nose grows. Till the time that happens (if it does), I submit that we assume that Pinocchio cannot be used as a marvellous tool for science, due to the distinction between a false statement and a lie.