It certainly seems to me that picking up and being able to use mathematical concepts without really being taught is a sign of mathematical potential. The approach you describe might be too scattershot to be convincing about what an appropriate placement is, however; that of course depends on achievement as well as ability. Might be OK if the school is flexible enough to commit to helping him catch up with any bits of earlier material he's missed, but they might reasonably want to see that he's secure on everything in level N before they put him in level N+1. What are you aiming for? If you want him placed in a particular class, it would probably be useful to google up a test of prerequisites for that level and make sure he can do them. E.g., Art of Problem solving gives a brief assessment sheet labelled "Are you ready for this?" and another labelled "Do you need this?" for each of its courses, which might be handy:
http://www.artofproblemsolving.com/School/index.php(Watch also for how much, if any, direction/correction/encouragement you're giving him as you work through the books: I find that with my DS there is quite a gap between what he can do with a minimal helping hand and what he can do completely unaided in a classroom. I think that's fine and normal, but one does have to be aware of it, and if you're using assessment tests, be clear which condition you're using them under.)
Good luck!
