It is a possibility. However, I've measured 86ms between east and west EC2 instances, 96ms between my client on the west coast and an east EC2 instance, and 15ms between my client and a west EC2 instance. Thus the additional latency per connection is only about 5ms.

For the total latency to be longer than 200ms, about 20 requests would need to be made on the same connection, which will not happen given the number of requests we do at a time.