I recently learned that Evernote’s iPhone app doesn’t download the info onto your phone or use up your phone memory – so you are in luck! Only way to put it on your phone and use up phone memory is if you go in and tell it to specifically download the notebook for “offline” use. Then that notebook is in your phone, taking up memory. If you edit it without an internet connection, the edits will not show up until you have an internet connection again.
The rest of the time Evernote iPhone app is just going online and pulling down your info for you from the web; you can edit your note on iPhone and Evernote is automatically syncing changes via the web so they show up on all your devices.