Waaaaaaaaaaaaaaaaaaaaaaay too different of a communication protocol. Just like you can't plug a HDD into an SD-card slot (which someone was going on and on on this forum for Wii U back in Loadiine-only days). And even if (and that's a HUGE if) someone managed to make a piece of electronics that would translate IDE/SATA communication to the direct communication that NAND has with 3DS, consider this - power. The 3DS charger is 4.6 Volt, battery itself is 3.7 Volt. A 2.5 inch laptop HDD requires 5 Volts, so this is already a problem. Next, battery drain. You know how people said PSP was a bad idea due to UMD drive eating a lot of power? HDD would eat even more. The battery life of that 3DS would be cut to 20% AT BEST.
In other words - nearly impossible and completely non feasible.
That's due to SD cards and 3DS's NAND are quite similair, that's why the hardmod has an SD-card as a plug, because certain models of SD-readers can read it that way.