WebSphere Process Server (as you probably already know) sits on top of WebSphere Application Server. Splunk has recently released a Splunk App that will assist in the monitoring of generic WAS, partly through the use of JMX beans. From a Splunk perspective, this is a scripted input that connects to WebSphere and periodically polls various MBeans inside the WAS JVM using the WSAdmin jython interface.
What you are wanting to do is definitely possible, as long as WebSphere Process Server exposes the MBeans you are looking to poll and index. But, I don't think the stock set of MBeans polled by Splunk would be exhaustive for a Process Server environment -- so some customization of the Splunk for WebSphere app would probably be required to really get to where you want to be. But, much of the framework is already built for your use.