Boomi seems to support a lot of third party things though Splunk isn't listed here. Dell has a "contact us" page for this specific use case, though - that of adding integrations. My guess is that one of the ones they already have should be able to be modified to move data to Splunk, since Splunk's so good at snagging random data formats. One of the listed ones may be some sort of JSON or Syslog dump to file, which should be all the Splunk needs. A bit of potential parsing and tada! The hardest part, and maybe this is partly what you are asking about, is what exactly are you doing in Boomi that you'd want to know about in Splunk? Session information of a sort? That is definitely an answer of "Well, it depends on what you are using it for and what you WANT out of it..."
Jitterbit's entire goal seems to be to enable integration, so I can't imagine it should be too hard to configure it into some semblance usability with Splunk. It could be as simple as dropping a syslog out of Jitterbit and letting Splunk read that. Splunk Answers can probably help some with that, but it'll take work on your own part. Still, I think if you get something working you already have a fanbase started! I am led to wonder if Jitterbit has any information in and of itself, or is just a conduit between other things. If the latter, well, maybe it's what you use to dump Boomi's data into Splunk?
The last - are you trying to tell me Adobe has an experience that we should care about? Lol, just kidding. This one's a bit harder for an "outsider" like me to understand. What data would you want to get out of this? It seems - and I could be wrong, this is just a guess from a quick look - that the Adobe Experience Manager isn't a thing from which you get data, but a framework upon which you build a solution and if that solution contains data you'd like, you use the framework as instrumentation to deliver the data you want in whatever format you like to the product you want to use it it. Maybe there's some information tucked away in it directly, but it seems your information is going to be largely driven by the stuff you are ... making available through the Adobe Experience Manager? Is that the right terms? Either way, if it's being used as a content manager to build websites, then you could integrate the Splunk integration HTTP Event Collector at each page or asset or whatever to feed in a bit of "session X user Y touched page Z at ABC time" type of information. Or whatever you'd want, it's up to you.
In any case, I know this sounds like only half an answer - and the half I've give you is "it depends", but that's where these things often start - snooping around to see what's available, thinking up potential use cases, grabbing the data you can reach and starting to play around with it. Sometimes you find products that there's just no useful instrumentation for because they're just a conduit through which others things act , so if you grab the right stuff from the endpoints you just don't need the middle because there's nothing new to be learned from it. Sometimes the middle pieces are the only ones you really need because all the actionable information is in there. And, usually, the answer is "it depends" on exactly what you are doing.
You are correct - AEM is a platform that you can build best enterprise scale web sites. Its a Java platform as well which means that you can add 3rd party Java JARs to it by wrapping them into an OSGi bundle and deploying that bundle.