Wicked is actually playing the Opera House, and in its past several visits, it did have some sort of lottery. There hasn't been any info yet re. a lottery for Hedwig at the Shubert.
Not sure about lotteries, but when i saw Once at the Shubert it did have rush, but when I saw Rent there it did not. So it seems to be hit or miss there. Opera House always has rush in my experience. Hedwig has had rush policies at most of its other theaters so thats a good sign, but hard to say for sure as that decision is made by the theater not by the show.