Account approval can be quick. I recall that when I signed-up (using PayPal for payment), my account was approved and ready to use in less than 15 minutes.
However, a lot seems to depend on how your application is viewed by the 'automated fraud detection system'. Some applications seem to be flagged as being a greater fraud risk (for whatever reason) and the available payment methods are limited. Sometimes Google Checkout is the only option offered and, as I said, Google can take a while to notify DreamHost of a payment.
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