In actuality, there's no such thing as "server deploys completely". Within a
J2EE webapp server, individual webapps can be started, stopped, deployed and undeployed pretty much at will.
In your particular case, the primary distinction is that you're only concerning yourself with whether or not a given set of apps is running, but not, for example, whether one of them has crashed and is no longer running at some point after the server had started them.
It's sloppy programming to create apps that fail if they cannot interact with external services. Unfortunately, this is an era where "Always the Low Price" and "Git 'er Dun!" trump good application design and implementation, so there are a lot of them about.
I suppose that a way could be found to gimmick up Tomcat so that it would bounce requests until otherwise directed. However, if I was entrusted with such a fragile environment, my first impulse would be to simply switch off the Tomcat HTTP and HTTPS ports at the firewall until the system had stabilized. That can be done relatively easily by an administrator without the need to come up with specialized code.