If this is just informal is it measurable?
I don't doubt it is effective however - it suggests alumni networks or diaspora like family networks (strongly suggested in China and India for example)
I know of at least one (non-software) corporation that spun off its IT shop, and that shop ended up doing rather well as an IT consultancy in it's own right.
Also, if you can reasonably spin off a division in this way, it isn't part of your competitive advantage, and it then has the benefit of allowing you to focus more on that.
(I suspect 'hamsters on wheels' comes closest, but it's not very mainstream.)
I think of YC as the modern equivalent of the old music business model: money gets advanced to potential talent, most of it disappears, some of it returns as a big hit.
The fact that the talent may be trading with other talent doesn't appear to alter that dynamic, because the money stays in the system, and you don't get a big hit until money starts coming in from outside the system.
I doubt any of the companies are formally bound to do business with any other by virtue of being in the Virgin group, but it would make sense that the companies enjoy some kind of (if only informal) "preferred vendor" relation with each other.
There's no need to describe it in theory as anything else than a number of independent companies, only with common ownership and perhaps a slightly above average interconnectedness.
Branson owns Virgin Management who are the central VC/Management corp. He has varying stakes in the other companies which vary from outright ownership, majority holding, minority holding, to brand licensing deals with occasional informal management input but no shareholding.
Bottom line is the different businesses are independent. Branson probably gets perks like free travel, and maybe some of the Virgin execs do. But I'm not aware of any loose internal market or preferred vendor relationship.
I'm trying and failing to think of an example of the model you're suggesting. (Which doesn't mean there isn't one - just that I'm not familiar with it. Maybe the recent Apple/IBM deal?)
It's an interesting model, but I'm not sure how well it works when customers can also be potential competitors. AFAIK syndication traditionally works better when relationships are distant and there's no immediate danger of competition.
For a startup doing B2SmallB, getting into YCombinator gives you ready access to a large network of customers. It's not just about access to investors, sometimes you can get very direct customer feedback by selling to your batchmates.