Is there a way to allow Dropbox as an exception to allow opening and executing of .bat files?
When system is locked down, you cannot execute a .bat file.

The only way to achieve what you are looking for is to use a background application that will run a script that does the following:

1. When necessary, download a bat file from Dropbox
2. Save it to a location on the local drive where executables can run
3. Execute the .bat file downloaded in step 3
4. Continue monitoring for a new file from Dropbox