So, The answer is a resounding YES — but only if you use the Repack feature.
Technical: "The HShop repack adds background download support and a wake-lock handler so downloads persist during device sleep, resuming automatically after network interruptions." can hshop download in sleep mode repack
When you close the lid of your 3DS, the system suspends most active processes, including the Wi-Fi connection and the FBI application, to save battery. Therefore, the download will pause immediately. So, The answer is a resounding YES —
