hd600's will be underpowered with or without the e7 so having the e7 will make no difference sound wise, esp if using with an iphone. The cheaper e11 will work though. The e7 DAC is nice to have when plugged into a laptop or computer or e9 but there are very few DACs that can work with an iDevice and the e7 is not one of them.
The E7 (or most portable amps for that matter) will definitely improve the sound from your 600s driven from your iPod. I own the E7 and HD580s and the Fiio gives more volume from my DAP (Sansa View) and an improved SQ, particularly bass.