Throttling does not affect packet latency. At the router level, it generally involves selectively discarding packets. Data is not drip-fed at the bit level or byte level.
In order to intentionally affect latency, it would have to do a lot more work by buffering them for a period of time before forwarding onwards.
Now throttling can affect latency of logical messages within a TCP stream depending on the size of those messages, due to the retransmissions required, but does not affect the latency of UDP packets as stated.