I stand corrected: encrypted PDFs are indexed unless a password is set. However, in the past they were unable to do so[0]: "Generally we can index textual content (written in any language) from PDF files that use various kinds of character encodings, provided they're not password protected or encrypted."
No, the PDF standard explicitly allows encryption without the need to set up user password; in this case, the owner password is set. The only change for the user is that the word "Secured" usually appears next to the filename in the reader.