Does Squirrly work on multisite installs, specifically ones with custom domains set for sub-sites?

Yes, Squirrly SEO works on WP Multisite.

You can optimize all the sub-sites in the network by activating Squirrly SEO for the entire Multisite Network or you can activate the Squirrly SEO plugin for a specific sub-site.

Note that each sub-site is considered a new website so you need to connect each sub-site from WP Multisite with Squirrly Cloud.