Well I would say that it's definitely doable. I was using JMX in an Apache Wicket application earlier with custom MBeans. Anyway MBeans is just a wrapper around some logic in your server application. So you can take the data directly from your application.
If you want to take an example how is this done in a working application you might want to checkout this:
https://github.com/apache/wicket/blob/master/wicket-jmx/src/main/java/org/apache/wicket/jmx/wrapper/MarkupSettings.java
The class basically holds a reference to the application and asks for data directly form the server app.
When the server starts up, then it registers all the MBeans through an initializer class:
https://github.com/apache/wicket/blob/master/wicket-jmx/src/main/java/org/apache/wicket/jmx/Initializer.java
Then every time when you take a look in your MBean server you will see the latest up-to-date information coming directly from the app.
There are some caveats though. One caveat is that Java in general doesn't provide any good abstraction to capture all Exceptions of a given type coming from any source of the application. You can register your catch-all exception handler but as far as I can remember it doesn't work perfectly.
What I was doing when I had to do something like this, I was using AspectJ to register an all catch place to handle exceptions. I was using compile time weaving to reduce the performance implication but I am not sure how much does it affect the overall performance (if it affects at all).
¯\_(ツ)_/¯
The other caveat is that JMX connections are usually difficult to set up in an enterprise environment. If you have to log-in through two hops just to arrive to the production servers because there are firewalls everywhere than your monitoring connection will definitely fail and you need to keep buying beer to your sysadmin and convince your manager that this is not imposing any security risk. :)
There is one thing though. You say
to monitor/configure a simple Java Client/Server application
You want to configure / monitor the clients as well? I've never done that. I am not sure that's even possible.