Not sure what you mean here, there is a massive gap between beating Airbuster, one of the first bosses in the game, and the parade in Junon. If you are referring to when Cloud is dressed in Shinra uniform about to join the parade then no, you cannot get Yuffie as you cannot exit Junon. Next time make the question clear.
// sorry, I meant Bottomswell, not Airbuster. My mistake. And no, my Cloud is not yet in the uniform. In this point you can still exit Junon but with only Cloud in your party.
/GG/ You should be able to. The Yuffie fight is considered a random battle. However, as I have never tried it, I do not know for certain.