We have 2 websites today.

One is at the root of the domain (domain.com) and the other is a subdomain (site.domain.com).

Each has their own set of users, with content and permissions specific to those audiences.

We'd like to automate login from one site to the other. So, when a user who belongs to site.domain.com attempts to log into domain.com, they get logged in and forwarded onto site.domain.com as a logged in user. Users that belong to the main domain.com should login and remain at domain.com.

Can I use Multisites Single Sign In to accomplish something like this?

In this specific case, the answer is NO.
The requirement to have the single Sign-In working is that you are sharing the Joomla users between the websites.
Here, you mentioned that each site have their own users. Therefore, as the users are not shared, it is not possible to share the login information between the website.

I hope this is more clear.