Sorry I didn't read your question closely enough. I was curious and did a quick look on the 'net but all I found were a few non-answered Stackoverflow questions (which may hint at the possibility that WebSockets don't work with packaged apps).
On the other hand, the official list of disabled web features (http://developer.chrome.com/apps/app_deprecated.html
) does not list WebSockets. Maybe the docs aren't perfectly clear on the issue though.