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.
When setting up a passphrase for your Ledger hardware wallet, you basically have two options: insert a passphrase every time you want to get access to "hidden" wallets or attach it to a PIN code, meaning that your passphrase will be recorded somewhere in a hardware wallet's memory and may be extracted and used after a PIN code was entered. In other words, Ledger adds a "Remember me" button for passphrases that essentially negates all the benefits of "25th word" and hidden wallets by making them publicly available for anyone knowing a short PIN code. Given that the Recovery feature doesn't make sense in cases where a user has set up a passphrase since a seed phrase alone is insufficient to get access to coins, it would make sense for Ledger developers to include a passphrase into this encrypted transfer scheme, especially considering the fact that it is equally important for a successful recovery and already sitting in a device's memory. Ledger developers could have issued malicious firmware stealing users' seed phrases and passphrases, but finally decided it would be more beneficial to create a service that people subscribe to and share private keys and identity information with absolutely voluntarily.