P!nk actually does have some acting experience. She was in a film called "Thanks for Sharing" about a support group for sex addicts. I watched it once years ago, but I remember liking the film a lot and finding her performance to be quite strong. It's an ensemble piece with lots of stars, and her storyline had her primarily acting opposite Josh Gad! She also appeared in a horror B-movie called "Catacombs", voiced a character in "Happy Feet 2", and has had some cameos in some other films.
Obviously, her resume is still light, especially for a role as demanding as Diana, but she's not entirely inexperienced with acting. Plus, she's always been an especially emotive singer, which may work to her advantage since next to normal is almost entirely sung-through. If this rumor actually happens, I'm cautiously optimistic that she can handle the role. My bigger concern would be that her daughter (who is TRULY inexperienced) could handle Natalie.