Nope anything 3DS only works on 3DS and 2DS, sorry. You'll have to upgrade your old DS in order to play it. It's the same for both the physical and digital copy. I personally prefer Physical copies, but it's personal opinion.
They did but playing a digital copies of DS-compatible games could still be possible I think. The reason why ACNL can't be played on the DS isn't so much the lack of wifi but that ACNL was developed specifically for the 3DS and there's no forward compatibility.