Don't do it.
But I am impressed that you had the guts to even CONSIDER singing 'Defying Gravity' a cappella.
I have known several people that have auditioned for American Idol.
(one of whom actually went to L.A.)
They all said that the people that most of the people that got called back sang songs that are mainstream and well-known, but not currently on the radio.
(They heard a lot of early-90s, and a lot of Motown. This might be partially because they all auditioned in Detriot...)
Doing Broadway will not get you on T.V. unless you're Frenchie.
Or maybe if you're as bad as William Hung.
(Keep in mind, the first two rounds of the competition are not judged by Randy, Paula, and Simon. The only people that get that far are ones that have the potential to be good for television. Hence why obscure songs are not the best way to go.)
If you decide to do something from Broadway, do something that at least has a pop-ish feel to it.
I starred in a short film called
Magnetic Personality. Check it out!