Is there a keyboard shortcut to open Notification Center and begin an iMessage as seen below?
The short answer is "no" but you can get around that if you try hard.
See this answer, Does Notification Center have keyboard shortcuts? for one way using AppleScript and Services. It refers to tweeting but the principle is the same for iMessage.
You can also set a keyboard shortcut to open Notification Centre then use
tab to move to the iMessage button and
space to open the new message dialog.