Hi Tuomo,
Thanks for reaching out. While the plugin doesn’t support network installs and full multisite management you can install and use the plugin individually, on any of sites within your network. Full multisite compatibility is on the roadmap and you can subscribe to the below GitHub issue for updates on this:
https://github.com/google/site-kit-wp/issues/276
In relation to WooCommerce you can use Site Kit with WooCommerce, as many of our users do. Just be aware that the plugin doesn’t provide any WooCommerce specific dashboards or functionality. There is also an open GitHub issue in relation to expanded ecommerce & WooCommerce functionality, you’ll find this below:
https://github.com/google/site-kit-wp/issues/459
Let me know if you have any questions with the above.