The simple answer here is that you should be able to reuse the form in the way you've described. The "surveying" obligation under the federal affirmative action regulations is to provide applicants and employees an opportunity to self-identify their race/ethnicity, sex, protected veteran status, and disability status. Applicants and employees are not required under the regulations to provide this information, and employers are generally not allowed to force applicants and employees to provide this information. In the situation described above, where it appears a new employee completes self-identification forms through employee self-service, a person who is rehired would find that information on race, ethnicity, sex, protected veteran status, and disability status has already been completed. The basic obligation here would be to re-offer the opportunity to self-identify. In regard to disability, this would mean the rehire would need to be presented with OFCCP's disability self-identification form. For other statuses, the rehire would need to be presented with a valid format for self-identification. The disability self-identification form and whatever form(s) are used for the remaining demographic data could show the previous values provided by the rehire, and the rehire could then change these values or leave them as they were.
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.