The DS does not connect actively to deployment clients (forwarders) and on its own it does not enforce anything. So whether DS is up or down does not have any impact on the immediate operations of the forwarders.
It's just that the deployment clients periodically connect to the DS and "ask" it whether there is an updated configuration bundle for them and if there is one, they pull one from DS and apply it.
So if the DS is not available the forwarder is simply not able to "call home" and ask for new config bundle.
It does not stop the forwarder or anything like that. You simply can't distribute new config to clients but nothing else should happen.