It would be great to be able to activate an application without showing it. I'd like to be able to activate Chrome to trigger a menubar action from my Desktop without using Show (which would navigate to my fullscreen Chrome window instead of my Desktop). Sending a keyboard shortcut to Chrome seems to be flaky, so I rely on trigger the menubar item directly.
Unfortunately I don't think accessing the menubar while an app is in background is possible (reliably). You could however use the "Send Shortcut to Specific Application" (make sure to use the latest BTT alpha)