Yakuake supports invoking the terminal in windowed-mode, if that's the profile you choose for it. I don't follow the purpose served by spawning an invisible background terminal; that doesn't seem to be common workflow, but I suspect you could wrangle it in your shell startup file so that the terminal self-invokes in hidden mode - but having 2 running copies (invisible and windowed) may result in both appearing when you press your global shortcut.