Yes, but with important caveats. The hShop installer for 3DS does support background downloading when you put the console into sleep mode (closing the lid), provided you’re using the of the hShop client (not the legacy .3dsx version).
Here’s a concise response based on the idea of an “interesting blog post” about whether hShop (the 3DS title downloader) can download in sleep mode: — An interesting blog post
However, there’s a catch: the 3DS’s native sleep mode pauses most network activity unless you’re using official software (like eShop or System Update). The hShop client works around this by keeping Wi-Fi alive during sleep, but battery drain is noticeably higher, and downloads may occasionally stall if the connection drops.
