No, you would probably just get access to the one box (and others identical to it). You generally would not get access to the other boxes, unless they share essentially the same vulnerability.
By "access" I didn't mean you would then have full access to everything on the network. By access I meant you would have an entrance point to the network and then would be able to access whatever other computers that the node you exploited has access to. Through that entrance point you would then be able to scan and attempt to exploit any computers it can access.
GP's point was that a monoculture can be devastated by a single assault, but a mixed ecosystem is much more difficult to damage severely.
So it is claimed, but there are numerous cases of people breaking through heterogeneous systems so this claim is a bit lacking.