Not directly. NaCl is a sandboxing technology that needs to recompile code according to strict rules that prevent the code from escaping the sandbox. If you can't compile the source, you can't put it in the sandbox.
You might be able to wrap the DLL in a native executable that exposes the functionality as a native messaging-compatible binary, then communicate with it that way. By design, this solution isn't going to allow wide deployment of your product using the Chrome Web Store, because it contains a Windows binary, which CWS doesn't distribute.