Yes, Post Pay Counter supports caching and is compatible with WordPress caching plugins.
Post Pay Counter mostly implements caching for plugin settings, user settings and active payment criteria.

Performance gain of caching

With latest releases of Post Pay Counter and its addons, server side caching improves stats significantly. We will update this page shortly with new results!

Under normal conditions, the presence of server-side caching does not seem to affect much stats page load time. I have run a couple tests, loading around 10k posts with only the Post Pay Counter plugin active, both with memcached active and not. From the total time cost figure at the bottom of the following screenshots, we see that there is not much of a difference:

In fact, caching is most effective when several users settings are needed in one page load. This means that if you often load the general stats page, and you have a lot of different users (maybe with customized settings), then caching will probably make stats generation faster. Otherwise, it is negligible. In my case, I only had a couple users.

With Post Pay Counter PRO (and other addons)

Most of Post Pay Counter addons do as well support caching. In particular, Post Pay Counter PRO does, as well as User Roles Custom Settings and Category Custom Settings (remember that caching is mostly for settings).

As before, we can see that in normal conditions stats generation, even with Post Pay Counter PRO enabled, does not improve in loading time with caching enabled:

The reason why caching seems mostly uneffective here is that stats are generated every time the stats page is loaded. In fact, no part of stats data is cached by Post Pay Counter. This is to ensure that stats always reflect real-time changes in posts and settings, and are always up to date. And yet, we still manage to load around 10k posts with the PRO version active in less than 25 seconds, which is great!