Hi mtbikelisa, Thunderbird is a mail client only. It supports the standard IMAP, POP3, and SMTP protocols for connection to mail servers. As long as Squarespace's mail service offers standard connections, Thunderbird should be compatible.

You may want to compare the settings with your client's current mail host to ensure a smooth transition. Also, you might be expected to migrate their mailboxes... Perhaps it's easiest to keep the same mail hosting and only move the website, if possible.