I am thinking about applying for the Dean's Grant for Student Research. Assuming I get the Dean's Grant and I am accepted to the Honors Program, is it permissible for me to do the same project for the Dean's Grant and the Honors thesis?

Although it is permissible for there to be overlaps between your Dean's Grant research project and your Honors thesis, the two projects cannot be exactly the same. You would be required to add an additional element to your project for your Honors thesis (e.g., adding an additional research question, including additional participants, or adding another measure).