Lock/erase stolen Mac only works after connecting to internet?

The commands to lock or erase need to come from you and get set up on your Apple-ID account (on the internet).

ONLY when the 'lost' computer connects to the internet can the 'lock' or 'erase' commands be sent to the 'lost' computer for execution.

So it is possible that IF the thieves who have your computer managed to break in and set up a new user account, they could be using word processors to create all kinds of documents, stealing your compute-power. But unless/until they connect it to the Internet, the computer can not receive the commands to 'lock' or 'erase'.

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Modern Macs are not trivial to break in to. The password you use to log in is NOT stored on the Mac anywhere. Only the already-encrypted version is stored. Your Mac does not even know how many characters are in the password.

When you enter a candidate password, it is encrypted as it is entered, and compared to the stored encrypted password, in the secure-enclave. All the password-checker can say is ¿was that it?

Follow these instructions: If your Mac is lost or stolen - Apple Support.

Stolen passports are a different subject altogether.

If the lost Mac is not connected to the Internet it might as well be powered down, for the purposes of remotely locking or erasing it over the Internet.

Your question has been answered. Please refer to If your Mac is lost or stolen - Apple Support and comply with its instructions. It explains everything that can be explained. If it were possible to answer your question with the binary choice you seek Apple would have so stated.