I'm not a Guitar teacher but I would be extremely surprised if nails are required for any Guitar exam. I strongly suspect that they are much more concerned with technique and (more importantly) musicality rather than whether or not you play with nails.
For those who aren't convinced here are a few examples of Players who play without Nails:
All playing 19 th century Guitars but there are plenty of people who play the larger modern guitar without the use of Nails. They are in a minority but they do exist! Most who play without Nails employ a slightly different technique, with string tension slightly lower than normally found with nail playing. I strongly suspect that the above players might pass an exam or two, even without Nails. :-)
As for 'decent tone' ? You have the harder sound of Nails against the softer sound of flesh. Bright sounding guitars will go some way to getting more of a Nail type sound - if that's what you prefer. Nothing wrong with playing without nails though. Perhaps it's a little like comparing a modern Steinway with a Chopin/ Schumann period piano. They have their own sound, not necessarily inferior.