The actual answer is going to be whether the Tony committee deems Cinderella to be a classic. Here is its definition:
Classics. A play or musical that is determined by the Tony Awards
Administration Committee (in its sole discretion) to be a “classic” or in the historical or popular repertoire shall not be eligible for an Award in the Best Play or Best Musical category but may be eligible in the appropriate Best Revival category, if any, provided it meets all other eligibility
requirements set forth in these Rules.
But one distinction between it and Flower Drum Song is that Cinderella has never been on Broadway before. Please don't misunderstand me, one can argue this either way, and ultimately we'll have to wait until the committee decides.
If anyone cares, I've attached the link for the 2012-13 Tony Rules and Regulations.
Tony Rules
CZJ at opening night party for A Little Night Music, Dec 13, 2009.