You want to bypass an internal amp and get to the line signal for two reasons: First, to get a cleaner signal. That means lowest possible SNR (Signal-to-Noise Ratio) and highest possible dynamic range. However, there is a limitation of how low noise can be and how much you can notice it. For example, going from 10% distortion (extremely bad) to 1% (which is borderline HiFi) is a huge improvement, while going from 1% to 0.1% is still a big improvement, but going from 0.01% to 0.001% will most likely doesn't make any difference in the whole setup, even though they are all 10x improvement. In the case of Nano 7G, there is simple no much noise in the headphone-out to begin with, and to get the best possible dynamic range, you simple make sure the volume is set to very loud. The second reason is to remove any coloration that the internal amp section might have. In this case, again, the internal amp section is very clean and free of coloration.
Since you will neither get a cleaner signal (that you can hear) nor removing any coloration, the conclusion is obvious: getting the line-out from the Lightning adapter doesn't improve the sound.
BTW, the DAC in the amp (E7 in this case) doesn't do anything to the sound of Nano 7G. That DAC only works with USB from a PC. You are only using analog section of the E7 (the amp section). If you want to get a DAC that supports iDevice, prepare to pay around $500 or so.
