Yes, you should be able to create Logging count measures for anything you are logging.
Just go to Logging (Under Events) and then when you find the particular log, right click on it and create measure.
One thing to mention, by default, we only capture 'severe', 'fatal' and 'error' logs. If your custom log is not at this severity, you will need to include them on the Logging sensor (go to Sensor Configuration on the Agent Group, find the Java Logging sensor and click on 'Properties').
Hope this helps,