While building the site, there was a button at the bottom that read "Publish."
The site is on a paid plain.
I got my answer when I receive an email from Squarespace saying the domain had connected successfully. When I went tot he domain, there was some copy that read "Private site." Once I hit "Publish," the site was finally live.
So yes, the site needs to be published in order for the domain to connect. I imagine it has to be on a paid plan as well.