You're right, it wouldn't be a problem because the local node would have all the files locally, and the URLs would all point to the local http gateway instead of an actual ipfs URI (we'd include the cid in API responses so you could resolve over ipfs if you wanted to, tho).

Users could also choose to disable remote ipfs lookups in the gateway for security/bandwidth reasons, but in the ideal end state we wouldn't even need a media proxy because the local gateway could resolve remote content.