I'm not aware of an explicit way to +1 a URL without using the GMS library. You can manually generate a share by passing a URL which might be helpful for you. As an example:
https://plus.google.com/share?url=http://example.com/
Will generate a share link for the site http://example.com. From Android, you could trigger the share by building the link and then encouraging the user to click it or by associating a share button with the action of opening the URL for sharing.