If everything was normal, it wouldn't matter what sort of radar the container ship had; they tend to run with "Iron Mike" (i.e., nautical autopilot) engaged once clear of harbors. In many cases, they don't keep a live body on the bridge, trusting to alarms built into (newer) radar units, or other ships maneuvering to missthem, or most often, blind luck!
And yes, that particular habit is incredibly dangerous. The only reason there aren't more collisions is the vastness of the sea.
Now, having said all that, I have to wonder what the hell the lookouts on the Fitzgerald were doing ... as well as the Quartermaster with the bridge watch and the guys in CIC! With competent lookouts, bridge, and CIC watches this should never happen! The fact that it did will cost the CO his career, even if he was asleep in his cabin, and will likely tarnish (at the least) the careers of everyone on the bridge at the time.