¿Se puede crear el botón de pantalla completa en cada página de archivo PDF?

No, it's not a part of the application, or the PDF file format. This is a button that the creator of the file added to it, and set it up to open the Full Screen Mode. It's possible to duplicate it to all the pages of the file, but only if you have Acrobat. You can't do it with the free Reader.

But you don't really need it. You can just go to this mode manually. It's under the View menu.

You can also press Ctrl+L to enter it.