This is one of the most basic principles of all Junos products - seperation of Control Plane and Data Plane, so that one does NOT lose mgmt visability under such circumstance. Both CON and Mgmt are connections to the CPU. The CPU has built-in protection mechanisms to either block or rate-limit such traffic, so that Mgmt stays up, either via Console or Mgmt IF Mgmt is on a completely separate OOB (you use term DCN - distributed control network?) that is not affect by such a storm or something else.
You can pump the data plane with as a big a storm as you like, and Concole and Mgmt access will stay up.
There are also recommendations for additional CPU/RE protection (see MX docs for sure) setting which obe would apply to lo0 interface, but a broadcast storm is already cared for. These additional protections can be apply to any RE/lo0 interface for any Junos product. The actual amount of additional support functions will depend on the exact product.