If what you had is just an amp, then nope, it sounds like you're good! Your Note 2 will do the digital-to-analog conversion, amplify it, output it via the 3.5mm jack, which you'll then run into the amp, and from the amp into the M100s. Now, it becomes a bit more interesting if your amp is also a DAC-- which yours is. The problem is that I don't believe the E07k has been confirmed to work without the USB Recorder app, which makes it suboptimal for music playback.
As an aside, IMO, part of the improvement in SQ in utilizing an external DAC is that you get an un-amplified output (even when the volume is changed, I believe it is done digitally), so you don't get the reduction in quality that comes from re-amplifying an amplified signal. There are vastly more knowledgeable minds about these matters here than mine, however, so I stand open to correction if it's warranted. (Obviously, if your cans can't run sufficiently from the Note 2s output, then you'd pretty much have to use external amplification, but I'd still wager you'd be better off using both your external DAC and amp. But your M100s should be fine.)
So I'd say if you can get the E07k to work as both a DAC and an amp, you'll be very well off! If you can only use it as an amp, I'd say your chances of experiencing significant improvements in SQ would diminish pretty dramatically.
Again, this is just my opinion, and I don't pretend it's even remotely as knowledgeable as some 'round these parts (lookin' at you, DanBa!! )
Im not very clued up on the digital side of things, However you're pretty much on the ball there.
By using an external DAC you bypass the sources internal amp and DAC,
So you're source basically becomes a Transport.
The external DAC's etc are usually capable of outputting higher bitrates etc ( I believe )
So you end up with a far cleaner sound and your rig is also going be more optimal :)
But like you said, There are better minds so please correct me if im wrong or right folks lol.