Would third parties know if I have my real wallet secured behind a passphrase?
Here is what Ledger say on the issue:
The Ledger Recover service, if used, does not backup your passphrase.
So in theory, no, the third parties would not know if you are using one or more passphrases. But this all depends on whether you trust what Ledger are saying, since I'm sure there will be zero way for the user to actually verify this.