Would passing data through a Restricted Boltzmann Machine before giving it to a Naive Bayes classifier improve performance?

I've been watching some lectures about Restricted Boltzmann Machines (RBMs) lately, and it occurred to me that one way you could look at them is as a filter that identifies and removes correlations in the input data.

Given that one of the flaws of Naive Bayes (NB) is that it assumes the independence of input data, it occurred to me that NB's performance might be significantly improved by passing data through a few layers of a RBM first.

Is anyone aware of any experiments where this has been attempted?