Does the API work that way now? The part on your own server used to only be for authentication and clients would then interact with reddit's servers directly. (Haven't done anything recently but used to maintain a moderation bot).
Currently clients talk direct to reddit's servers. But if reddit started billing for API requests, you can bet every appmaker would run a caching server to reduce the number of API requests.
Or they'd do some kind of peer-to-peer caching between clients.
