Start by making sense of the question.
What is white light?
What does continuous mean for a spectrum?
With my own vocabulary, the question looks strange. I would simply answer "yes" because the observed spectrum would certainly contain some continuous parts and therefore I would say it is continuous. But if you have a clear definition, you could do better.
I advise you to be pragmatic and simply explain how the observed spectrum would look like to the observer. Will it be different from the original white spectrum? And why? And how would it look like? ... and finally -if you want- decide about "continuous", but this is not the most important thing.