FAQ: Can I keep an Adobe Password on my PDF if I protect documents using Safeguard?

No.

When you protect a PDF using Safeguard you will be asked for the password to the file.  Safeguard will then remove this from the PDF file when it protects it so users will not be asked to enter a password when viewing the secure PDF file.

The Adobe Acrobat password does not provide any extra security which is why it is removed.