There is nothing that stops you from inserting stuff in the HTML document outside of your assigned element, though I would advise you to be very careful when you do this, so that you don't leave stuff behind when your extension is removed. A better solution would probably in most cases be to keep your content within your element and use CSS to position it the way you want.
Couldn't get the CSS approach to work so I added the tooltip to the body like you suggested. To not leave the tooltip behind, I added it while not in edit mode and removed it in edit mode. Used a function to calculate the offset from the container to the body to calculate the right position.
Thanks again for the help.