Yes. All jobs that meet the criteria outlined in Sec. 60-4.3 Equal opportunity clauses (all positions except executive and top management, those positions that will be filled from within the contractor's organization, and positions lasting three days or less) need to be posted with the State Employment Service. That includes any jobs that are filled by referrals from a third party recruiter.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.