Having two document ready doesn't make a difference here. You could have one document.ready and/or call Test.FUNCTIONS.init directly and all should work, and the fact that they are in different namespaces doesn't matter as well.
As for why you're getting undefined, I think it is probably because your chunk_of_markup variable is actually undefined at that point. My guess is that you're getting the value for it through AJAX and so the call is done asynchronously which means the DOM will be ready before it actually returns a value. When you use the Debugger then the value is evaluated at the point of time where you run the command so by then, the async call already returns successfully (it's a race condition, if you're fast enough and your AJAX is slow then you can still get undefined, and it's also why 2 ready functions happen to make it slow enough for the AJAX call to return but it's still unreliable).
In all cases, if my theory is correct, then you need to hook to the callback of the AJAX request rather that DOM ready event, this is the only place where you can guarantee that your variable is defined.