Hi Barry and welcome,
Well, anything is possible if you want to write code, but why bother with the exe? Just create a config XML that the exe reads in to run. That's a more data-driven process and simpler too. InfoPath is great at generating XML and your exe can be written to be data agnostic. Just have it load the config and run off of that. Then, you can have a button in your form that saves the XML and runs the exe. This will require full trust. Another approach is to use a workflow to kick off the exe as a custom action. That way your IP form doesn't have to be full trust.
Or, you could install a task that monitors a folder for XML files and runs the exe. Lots of approaches to trigger without doing the InfoPath button full trust option, but that option also works.
Happy trails,