Instead of using online/offline sensor that stops the script, make a block that is like:
online?
And it will report true or false.
Offline
That's an idea.
Offline
What would this block be used for, though? In Scratch 2.0 (the next version of Scratch), projects will run the same way online and offline (since they'll both use Flash), so there'll be no need for downloading a project to run it. There'll be a fullscreen mode for online projects anyway.
Offline