I don't know the geek term for what I have in mind (widget? headless? whatever??) .. Expanding on the functions of the dashboard widget might be one approach, but for me at least I think I'd rather a menubar function.
I'd like to be able quickly access some basic functions of Accordance without needing to launch the full app, which takes quite a few resources. I actually find it easier to bring up a bible text on BibleGateway than to launch Accordance - if all I want is a quick look, copy, paste, etc.
Apart from that, the particular function I most use is adding user notes, which I like to do while having my devotions. I don't want the distraction of needing to launch Accordance, open a text window, use the context menu ..... etc. I'd like to be able to just click an icon in the menubar, type a note to a verse, and save it.
Other users would no doubt have other functions they'd like to access quickly and move on, so I guess there could be many functions for such a 'mini app'. But these are the ones I at least would like.