Internet connection required to work with the new Projucer?

You can use the Projucer in “GPL mode” - see this thread: Will Projucer and JUCE always require sign in?

If you are paying for JUCE, or are using JUCE under the terms of the GPLv3, then the splash screen and analytics are opt-in, not opt out. If you have a Personal license then they both have to be included, it’s not optional.