I’ve found next to no information on whether the rest API works with Wordpress multisite setup. Does it?
Yes, the REST API is in the same location, just append
/wp-json to the end of a site/blogs URL and there it is
As for the network admin, at the moment there are no endpoints explicitly for multisite, so you can't use the REST API to create and destroy sites without building those endpoints yourself, but this may change in the future