natures swiftness doesnt trigger the GCD skribs, so it really is nearly instant, adjusting for lag.
there are rare times (very rare) where ive been able to kill or have been killed after using NS but before HT goes off, so there is a very small window that lag creates, but for the most part its about as instant as youre going to get. the NS'ed HT will go off and heal someone a good second before the GCD refreshes.