Not it doesn’t.
Only domains with “active” popups are counted as part of your plan.
So for example, if your plan allows 5 domains, you can have 6 domains saved on your account. But only 5 can have active popups at the same time.

By the way, the page views counter works the same way. Even if the Remindee code is in your website, page views are not counted if your website doesn’t have at least one “active” popup associated.