Transferring Domains and Emails

I have a squarespace site already and 2 third-party domains that are in the process of transferring to squarespace. I want to transfer the email addresses associated with those third-party domains  as smoothly as possible. Do I go ahead and sign up for emails with squarespace?  They will be the same email addresses as they were on the third party site. Or wait until the domains officially transfer before I do that? I want as little interruption in email delivery as possible. Thanks for the advice!

I am also interested in this topic for the same reasons.