With HTTPS, tracking will be more accurate.
The thing is, when a user goes from an HTTPS website to an HTTP one, most browsers hide the referrer information from the HTTP site.
This doesn’t allow Google Analytics and GA Connector to track the source of such user (unless there are UTM parameters).
So if your website is still HTTP, and your user is coming from some HTTPS blog for example, GA Connector (and Google Analytics) will consider this user’s traffic source direct/none.
You can read more about this and other tracking details here.