The client just jets out a single UDP packet. There is no TCP setup latency,
effectively no latency at all though
only from that client's point of view.
I think it is a valid claim, but only for a rare set of use cases where the significant caveats regarding delivery & response are OK. Though of course those caveats are not as heavy as they might at first seem if the link between client and proxy is strong and reliable, because the proxy will be performing the full handshake and can manage redeliver on error and other such things - but the client doesn't need to worry about any of that.
