I have tested it on a multisite environment. So far everything is working correctly.
It will be great if we can have centralized control and dashboard on the main site. So we don't need to checking it on every of the sub sites.
For even better, on the visitor log users can choose to see activities of all sites or to filter the result for a single site only.
I know Imsanity plugin has good multisite support, and I found this discussion that contains good information how to do it, hope it can help: