Yeah, you can definitely use this with recurring payments. Once you attach the token created by the Checkout to a customer, you can bill the customer whenever you like. (There's more at https://stripe.com/docs/checkout)

That link is broken (has an extra period).

Thanks, fixed.

Checkout simply creates a token, that you can use to set up a one-time payment, recurring payment, or even to just create a new customer object in Stripe.

I wasn't able to find any documentation about using the button for recurring/subscription billing. I hope that's a feature coming soon.