Yes you can (or not) using the experimental APIs chrome.experimental.webInspector. http://code.google.com/chrome/extensions/experimental.html
You can even change the content and panels of it.
Note that you will not able submit extensions that use experimental APIs.
This is quite old but since I stumbled upon it now searching for a solution I figured others might have too. Since Chrome 28 you can use the devtools.* API. This allows you to open and manipulate DevTools panels. It is also notable no longer expirimental.
It's not impossible with side extension, but if the reason is that you've tired to click Ctrl + Shift + I again and again every time - you can simply open the right button menu on needed page and select "Inspect" from it, it'll open the console like extension button, and also you don't need to search for its icon every time you need it, which is more conviniently than using an extension.