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

YES, but it’s important to note that:

Even though they are part of the same WordPress installation, Squirrly SEO treats each sub-site as an individual website with no connection to the others within the Multisite network.

Since each sub-site is considered a separate/new website, you’ll need to connect each one from WP Multisite with Squirrly Cloud.