A plain vanilla Integrity Jenkins configuration should checkout everything under a project, unless the "Exclude List" option in the job configuration explicitly specifies .pj to be omitted (or vice versa, the "Include List" specifies only certain file types to be checked out). I presume this is an Integrity Server version below 10.8? Can you specify the ILM version and the Jenkins plugin version.
Also, what is the use case for populating the workspace with project.pj files? They ordinarily wouldn't be required by Jenkins for any build activities.