@scottalanmiller Sure! My minecraft plugin does this. Using the action:widgets.loaded hook for loading the initial data and appending it via jQuery using the data-widget selector, then I update the data using websockets and/or a setTimeout with an ajax call.
For @planner, this script can be placed in the "Global Footer" widget area (or any other widget area present on all pages). It overrides the ajaxify method and returns anchors to their default operation, which is a regular page load.
Depends, if you're doing largely front-end code (like embedding an iFrame to some chat application) then a widget works best. If you want to modify the API or save things into the database, then a plugin is right for you.
I think your best bet is to figure out what you need to do, and then find a plugin that does something similar, and modify that plugin, or take code from it (it's open source afterall ;))