Yes, if your organization is subject to the OFCCP's affirmative action regulations for protected veterans. According to the regulations at 41 C.F.R. § 300.5(a) all employment openings must be listed with the state employment service delivery system. "Employment openings" includes "all positions except executive and senior management, those positions that will be filled from within the contractor's organization, and positions lasting three days or less," and includes full- and part-time positions as well as temporary positions. So unless your paid internship falls within one of those exceptions, the OFCCP will expect you to list such openings.