No, apologies, but this is not possible.
I’ve set things up like this because, in WordPress, you cannot have more than one paginated query on a single page. If I were to add this functionality to a shortcode, then the user would be free to have post as many instances as they wanted, and things would break.
Allowing you to use the Builder is a little different because I can actually force you to adhere to this rule. When you’re in the builder, try to insert more than one paginated element into a layout, and you’ll get an error. However, if a paginated element were integrating into a shortcode, this check would not be possible.