Application for Membership plugin

I am developing a not-for-profit site that supports military veterans. This org provides multiple services so I’ve developed a multi-site. One of the services is online training which will be purchased for the veterans by corporate sponsors. I need the veterans to register for the online training for which they will have access for 2 years but they do not pay for it. I need to also track the registrations. Is “membership” an over-kill for this application? If so, what would you recommend would be the best approach. I need to distinguish between registering as an ordinary visitor of the site and a veteran. Only veterans will get access to training.

Also, if “Membership” is the best approach, are members site specific or is there an option to have a membership to all sites in multi-site?

Thank you.