The reverse will work, but there wont be any improvement in sound. In fact, the signal is already going through the cr4p little caps inside the ipod, so it gets their characteristics anyway. The caps in the Imod LOD is likely to only worsen, cause generally, all caps worsen. just some worsen less, and some worsen favorably
But, yes, you can use the Imod LOD on a normal Ipod and you can't use a normal LOD on an Imod, as you speculated.