I teach at community college. I often publish the homework problems at the beginning of the semester, listed by section.
I have never had a student work ahead (that I know of). And I have had a few students who loved math, asked deep questions, and were interested in doing extra. I don't think that is likely to happen, except in very rare instances.
I am assuming you mean that answers are not available in the back of the textbook for the exercises assigned. If no one does find research on this, it would be pretty hard to test. Students have access to photomath, which can solve their problems for them.