There is no way to do it today. But I am interested if you could elaborate a bit on your idea. Don't you think that adding a border around annotations could easily clutter the schematic? A mockup of what you have in mind would be helpful. Thanks.
As my colleague Olivier pointed out, automatically sizing boxes are not currently a feature in the tool and could look messy. However properties inside an outline have long been supported and are in fact required for border symbols. Below I have created an on-sheet link symbol demonstrating text inside of an outline. For best viewing when annotating, control the text lengths, correctly use text origin, use a placeholder on the symbol, and the reposition properties RMB selection.