Good for them. The asynchronous master-master replication dynamic of couchdb is exactly the right solution for a barely connected federation of clinics. That said, the last paragraphs talk of "instant" as pointed out by Maro is a touch disingenuous.
That's basically the point, without CouchDB, they don't have internet, because the connection is spotty, power goes out, and latency makes it unusable when it does work. CouchDB fixes all that.
Your software will time out long before a packet arrives. You could make your (custom) software never timeout, but your software is likely to become unusable due to pauses whose durations are unknown - what if it takes 5 minutes for a small operation to complete?