No ethical problem at all. You bring people into the lab and have them learn something. You don't have to go into the classroom and mess with their actual educational experience. Cognitive psychologists do this kind of research all the time (thoroughly vetted and approved by ethics review boards).
Rigorously designed studies
have been done, and have found no benefit from matching the learning experience to the learner's supposed learning style.
Here is a review article, and
here is another that goes into more technical detail. I'd be happy to share the complete papers with anyone who wants, just PM me.
