I don't think an alumni association is the same as an old-boy network.
An alumni association is an official group. When you graduate, you pay a fee to become a member of it (and then you get a slick magazine and lots of fundraising appeals). If you are the kind of alumnus who cares about things like college sports, you might use the association to become active in lobbying the university for, say, a new football stadium. Or if you are the kind of alumnus who is extremely proud of your university and still has sentimental associations with it after decades, you might host meetings of other alumni in your area, sponsor scholarships, help recruit new students, and so on. But for most people, it's basically an inactive group, just a list with your name on it.
An old-boy network is an informal, behind-the-scenes network of people who know each other, or know someone who knows someone else, and who use those connections to their advantage in business and social life. As the word 'boy' suggests, it refers in the first instance to alumni of all-male schools, usually exclusive boarding schools where wealthy boys wear blazers and ties and are groomed to be the future leaders of society (= public schools BE, prep schools AE), or perhaps also the oldest, most established universities, which were formerly all-male.
I agree that 'old-boy network' might be a useful term to add, but I'm not sure there's going to be a single short German translation.