If I were to resend an envelope after one of the signers signed, would it start over and require that first person to re-sign?

If you select "Resend" on an envelope, it sends a new email notification to the current active Recipient only and does not email Recipients who have already completed actions nor does it start the entire envelope over. Here is an article on the Resend feature...

https://support.docusign.com/en/guides/ndse-user-guide-send-reminders