Nope. Even free apps need to be "purchased" and Amazon uses the billing address associated with your payment methods to ensure you live in the region they are licensed to sell them in.
Sometime all you need is a billing address in your 1-Click Payment Settings. But, you may eventually need to verify it with a credit card (or debit card with a credit card logo, or pre-paid credit cards work).
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I'm being extremely clever up here and there's no one standing around looking impressed. What's the point in having you all? - Dr Who