Not sure I understand your request exactly. If you run it as a system service, which is totally doable, you manage it as a system service. So you have to have administrative privileges to stop or start the service.
If you want to run something as system service but control it from an unprivileged user account, I am not sure how you would do that without having the needed privileges to control a system service. Then you may be better off using OpenVPN GUI as it comes by default; where the program to control OpenVPN process runs as unprivileged user, but any privileged actions needed to be performed by OpenVPN like setting routes and such (which requires admin privileges) are handled by a separate system service built for that purpose.
