The short answer is ‘I don’t know’.
Having never worked on a WP Multisite environment before myself, this is something I’m going to have pencil in and play around with for a future release of this plugin.
The plugin does not create any custom DB tables, and plugin data is saved only using the built-in WordPress Custom Post Type action hooks. Data is therefore saved to the standard WP ‘posts’ and ‘post metadata’ tables. I’m not sure how this would translate to a multisite environment, and whether using the standard Custom Post Type action hooks to save plugin data will cause WP to automatically sort things out within a multisite setup.
It will be interesting to find out though…