Not really. While they do benefit and improve with additional amping, they certainly don't bottom out like what seems to be happening with you. I've ran mine on underpowered mp3 players, and the result is the sound being clearly less resolved and quieter, but everything's there.
It might be related to your DAC. When you get the E11, try setting source volume to 75-60% and increasing volume through the amp, that should fix your DAC issue.