I can confirm that is how it works.

Since I’ve been basically studying the system transfer process non-stop and watching so many people do it in videos. I know that is how it works, as I saw a video where a guy was in this exact same situation.

You are correct in that all you need to do is go to the eShop afterwards to re-download the game. The pre-installed game will merge with your account on the New 3DS after the transfer is complete.