I think you could...it's pretty easy. Can you read music at all? It's not required, because they even make music with the finger holes demonstrated that you cover up.
I feel like a pusher...
Hey dude...try this whistle, man...it's a goooooood whistle...
LOL You're a baaaad influence, you know!
Not only that, but once you've been playing a short time, you may be able to figure out a lot of songs on your own. I'm not as good at that as I should be, but given time I can usually figure out how to play songs I know well without any written music.
My sister doesn't even really read music - she plays entirely by ear, and can pick up new tunes that way amazingly fast. I wish I was better at that...on the other hand, I have access to TONS of sheet music that she has trouble with, so there are benefits to both methods, I guess!