No, it would not. Please read my post again. The webserver would not have login credentials for the password management machine. Additionally, I object to your

No, it would not. Please read my post again. The webserver would not have login credentials for the password management machine. Additionally, I object to your implication that any network service can be trivially compromised with "one more round of cracking". This is a view of software security that is propagated by science-fiction movies, and is not grounded in real life. Vulnerabilities that permit remote code execution are relatively easy to prevent by taking appropriate precautions when designing and implementing a network service, and almost every such vulnerability has its root cause in doing something obviously insecure (e.g. writing in C/C++ or a language with eval(), passing user input into an OS procedure).