R&P: Does Green Day's 'Insomniac' album sound like it could get away with some Grunge in the genre?

People say the "New" Green Day is not punk. I always thought they were punk, but never the 'typical' punk rock (Anti-Flag, Social Distortion, Rancid, etc.) I think Green Day always had more of an alternative sound even since their first album Smoothed Out. Anyway, if I knew nothing about punk rock or Green Day and if somebody were to hide "Brain Stew" inside a CD full of Nirvana, Soundgarden, and Pearl Jam. I could definitely mistake it for a grunge song. If Green Day came out with Insomniac today, I could see them and Foo Fighters doing a tour together.