Nah, it would typically include all info known at send time, but it can see if there is updated data on email open time.

E.g. when you open a notification email from GitHub, the email can tell you that since it was sent, there are now additional comments to consider.

I doesn't have to connect. All email clients I use are set to block external content, unless I explicitly decide otherwise (but I can't remember when I last needed to see an image included in an HTML mail).