This is a simple question. But, we can face these kind of simple questions in Open Ended Section of Lab exam. Undoubtedly, Handling and Interpreting questions is one of the vital skills to pass the CCIE Lab exam. So, when I read the concept of technology, I try to ask questions to myself of what and how the questions will come. And I believe that this habit makes me more clear and understandable of technology what I've read.
Let's back to the answer of that question! VTP password will not propagate via VTP messages. You can verify by checking Configuration Revision. Configuration Revision does not change when you change VTP password. And so, the VTP password must be configured statically on all switches.