Unless you expand the text no. That's the old gag of the font's em box vs the actual contours. If you're really doing this a lot and always use the same fonts, though, by now you should have figured it out and hardwired the sizes into some paragraph styles or created scripts for your workflow.
Thanks for the response. We have little Illustrator experience - we are software developers here.
We have been looking into the scripting method but cannot find out how to check if the text has overflowed. In InDesign there is a property called "overflows" on a text area that would allow you to loop through re-rendering the text until it overflowed and then reduce it a bit. This functionality does not appear to be present on Illustrator.
I'm not sure where to look for help on this now!
This script can correct rectangular text boxes:
Maybe the code gives you a clue.
Also there's a plugin that can detect text overflows: Text Overflow Alert for Adobe Illustrator - Macintosh
So if scripting does not get you there, you might need to write your own plugin.