On the Today Show OTTC went with bit of Life It Like A Train, and then they did part of Babette and surprisingly i think it actually worked pretty well. They only did the bit after Lily decides to do Babette over Mary Magdalene, so it's "just" a fabulous, fun production number that doesn't tell you much what the show is about.
But since that did not include either Peter or Andy (who seems likely to grab a nom I think), it still seems unlikely for the Tonys. If they want Andy featured, they will most likely be "Sign, Lily, Sign".
I'm wondering about the 2 shows that already performed at last years Tony Awards, The Last Ship and Finding Neverland. They definitely should do different numbers this year, if they perform again (in the case of TLS, FN surely will)