Q: Does PDF Studio support the top-level menu, called the Unity Global Menu, of Ubuntu?

A:  Yes, it can but you will need to install Jayatana which will automatically put the menu at the top for PDF Studio as well as for any other Java application.

To install Jayatana, open a Linux terminal and type in the following commands:

sudo add-apt-repository ppa:danjaredg/jayatana
sudo apt-get update
sudo apt-get install jayatana

Then log out and log back into Ubuntu.

Read more about this at this link:
http://www.webupd8.org/2014/02/get-unity-global-menu-hud-support-for.html