Don't have a clue. The manga has yet to give any indication that he will. I assume that he will,............eventually.
i think kishimoto has no intention to make naruto a chuunin or jounin.
maybe he plans to make naruto like gaara, from genin level ninja to kage level ninja, skipping chuunin and jounin.
tsunade will have to give him an exception because you need a genin team first of all to participate in the exam to begin with, and even if he does get a team he will rape the other genin with his rasengan and his sage jutsu. if that doesn't happen then he probably won't ever become a chunin.
i really don't know about that....i mean, i think he need to take another chounin exam or tsunade will make it exception and appoint him as a chounin without taking an exam! i mean naruto already so strong than to the other genin will take chounin exam because he already master some difficult technique!