Hey Brian,
It's a good question and in a simple answer yes it is possible.
But I would see this being a plugin. If we're talking about the jQuery UI tooltip plugin and you wanted to add it into core core - let's say you want a tooltip on hover of the menu button - you would want to listen to an event and tap into that event. This way you're not affecting core code and are instead enhancing Adapt with a plugin. This is the preferred route that we suggest you take.
We also have a conditional loader that pulls in the different versions of jQuery so core serves up v1.* for older browsers and v2.* for newer versions. These jQuery versions will get updated whenever a core release is issued.
After Learning Technologies I would really like to give a demonstration of how easy it is to add/enhance Adapt through the use of plugins. I'll post up here with the details in a couple of weeks.
Hope this helps and feel free to ask anymore questions.
Thanks,
Daryl