Why do you need an Internet connection when running on a local port and IP?
You don't and it is totally unrelated. Same as having outdated flash player doesn't impact C2 at all, it just impacts your browser and shouldn't be an issue when previewing HTML5 anyway.
All I can think of for the low startup is the startup page of C2 since it is based on IE.
Make a test, disable the startup page from the preferences, disable the WI-FI and launch C2 again.
Do you see an improvement ? If you do, it is safe to assume it is the lack of internet that slows down IE's browser and C2's startup page as such.
If you can spare that startup page, remove it from the preferences and you shouldn't have issues any more.