I had a look and it seems Apple doesn't allow text entry in notification center widgets. That's unfortunate...
Maybe use Alfred as a Dashboard replacement for text entry? You can set up workflow scripts that can do pretty much *anything* on the Mac, and loads are prewritten for things like Evernote text entry. For instance: "Cmd+Space" to open Alfred, type "enn This is a new evernote entry" (with "enn" being the prefix you chose to trigger the evernote workflow), and hit enter and it will be added to Evernote. You can even configure hotkeys to bring up alfred with some prewritten text; so you could do something like "Option+X" = opens Alfred with the letters "enn " prewritten and ready for you to write more text. So it's faster than Dashboard. Have a look at it.
Here's the official Evernote workflow:
http://support.alfredapp.com/evernote
I use Alfred constantly and have set up things like "Option+X" = opens Alfred with the converter keyword prewritten; so I can type something like "Option+X $100 EUR" to get the value for 100 USD in EUROs, or "Option+X 1 foot meter" to get the size of a foot in meters.
It can also control media players, launch applications, find files and act on them (like open, open with application X, open terminal here, show in finder, etc).
Alfred is yet another reason why I never use Dashboard anymore. I had forgotten OS X even had Dashboard and when I opened it yesterday, I was greeted with years-old widgets. Embarrassing... ;-)