Can you have Mail Merge work if your Word uses a drop down box?

Your document contains a mix of formfields and content controls. Formfields and content controls should not be used in the same document as they weren't designed for such use and trying to do so is a known source of problems. In any event, text formfields can't be used in a mailmerge.

In answer to your question though, no. That said, since you're trying to generate the output from a mailmerge, I'd question why you need a dropdown instead of just the mergefield.