Yes, the same ambiguity works for me. It would be strongly biased by intonation, I think, though.
"None of the students" would be the more naturally way to indicate that no papers have been submitted, so the default interpretation is probably that SOME students have not yet (but some have), especially if you add "yet" to the end of the sentence.
However, structurally, I would like "all" to take wide scope, so this makes the sentence somewhat awkward. The same applies to "every", though, and (1) is awkward in the same way, but I'd say (1) is more likely to be interpreted as "No one has" than "Some haven't yet".
