Hi,
The plugin does work with multisite, although that’s not been our primary focus so some odd behavior may occur (further multisite development may happen at some point though), so I can’t in good conscience say that I recommend it on multisite at this time.
You can activate it individually per site, or network activate it they both work but it’ll only be accessible from each individual site and not the Network Admin.
The permissions to access troubleshooting is tied to site-administrators, so admins of individual sites would be able to use the tool as well when it is active at this time.