No.

Just no. No no no no.
NO.
It's a nice song, but:
1. It's the weakest of the album.
2. It'll probably be nice live and will show doubters/ignorant people from GP that have only seen one performance or something that she can sing, but it's not the best song to use.
3. She NEEDS to do a single.. even if it's Applause.. this will be online all around the world and could be massive opportunity to truly bring Applause/DWUW (back) to life.
4. Isn't she doing a live music video? It's not gonna be too interesting with a ballad...
At least do a medley with it.