It's definitely possible to do; however, since twitter turned off Basic Auth, you'll need to setup a twitter 'app' that you'll grant access to (oAuth) then use that to post. It adds a bit of complexity, but it shouldn't stop you.
Of course, if your CMS can provide an RSS feed of updates/additions (perhaps based on that update page), you could use one of the many RSS to Twitter posting services.
I'm a big fan of the way you can pick and chose Zend Framework's components, so I'd probably use Zend_Service_Twitter for something like this; however, the concept is similar on any Twitter library (or even just interfacing directly with Twitter, but that seems like unnecessary work).
First - as mentioned - you'll need tosetup an app on Twitter. The developer site should help there. You'll also need to **grant your new app access to the account you'll be posting to, what you need is an oAuth access token.
The access token is used for read/write, you'll use it to setup the Twitter library (again, an example from Zend's documentation, but it should be similar to other libraries):
$twitter = new Zend_Service_Twitter(array(
'username' => 'johndoe',
'accessToken' => $token
));
Then use whatever data the CMS provieds to create the 'update' post. Maybe something like this:
$status = "We just updated $projectName, check it out: $projectShortLink";
$response = $twitter->status->update($status);
Of course you'll need to make sure that's under the 140 limit.
It's pretty simple, the real overhead is setting up an 'app' and getting the oAuth token You'll need a simple one time script to request and retrieve the token (Zend's documentation gives examples) Or you could request permission for xAuth, but that seems a bit over the top for your application..
One potential benefit - since you're creating an app, you get to pick the 'via AppName' that's displayed in various clients.