There is nothing in the servlet spec for dictating which apps get loaded first. I don't know if any containers provide their own way to do this. I use Tomcat and I know it doesn't.
Unless you know that the container that you're using has a way to control the order of app deployment, you should avoid having one app depend on another; especially during startup.
You might want to have this initialization take place when a servlet is hit for the first time. If you do this, you should also have a way to gracefully handle a situation where the servlet gets hit before the dependency app has started. Something like an error page that asks the user to try again in a moment.
Another option is to run two separate container instances, one for each app.
As Bear asked, why are you doing this in the first place?