I've just migrated one multisite installation and it worked except for tables
$wpdb->site (plus one usermeta field) where URLs didn't have protocol and since this plugin searches for whole URL those fields weren't changed.
So, value in those fields was
example.com but setup suggests URL
http://example.com which means that plugin won't even look at those fields since they don't match search criteria.
I suggest that plugin takes into account domain name and not just whole URL since this will affect fields that don't use protocol for any type of installation, not just multisite.
Removing protocol from setup form isn't best idea since someone might want to change protocol of the URL, from HTTP to HTTPS or vice versa.