100% of the calculations are done in the browser and the MME servers are not involved at all until it becomes time to record the results in the annotation.
Doing a lot of measurements in a row may be taking up system resources but as long as the piles are all close together it won't be redownloading the depth data since it is already cached locally.
To be honest, it probably isn't optimized for doing lots of measurements consecutively. We will have to look at that. Reloading is the correct course of action for now.