Let's say I have a "John Doe - $5 USD" IOU pending. John Doe does not have $5 USD in the gateway, but he does have 5 dollars worth of BTC in a gateway. Will the gateway automatically sell John Doe's BTC to pay me $5?
Gateways don't automatically do anything. What you want to ask is whether or not Ripple can find a path that allows John Doe USD IOUs to be converted into Gateway BTC IOUs. If Ripple finds an appropriate offer in the respective order book or order books (considering all combinations of conversions) then yes.