Turns out this was a pretty stupid question. Didn't realise the UI node could also be clicked in the doc navigation tree. The desired functionality is actually built-in. See the relevant doc page here: http://tidesdk.multipart.net/docs/user-dev/generated/#!/api/Ti.UI
You have the following methods to achieve the desired or related result:
- Ti.UI.setBadge(txt)
- Ti.UI.setBadgeImage(imageURL)
- Ti.UI.setDockIcon(icon)