Great question, I can't believe Coachella doesn't have a well-organized, easy to understand FAQ listed on their website under an easy to read title, maybe named something like "Festival Info and FAQs". Huge blunder on their part.
Which is to say: no, you can't. If you remove the water pouch you can bring in the bag, same as any other backpack.
I saw several get confiscated starting on day 2 last year. I also had an (empty) squirt bottle fan thing (plastic and foam, no metal) that got taken at the gates. Beware. (also, they started checking under people's hats last year too, so beware)