While the SS Californian did try to rescue Titanic survivors (and it's from the Californian that we knew the ship broke in two), it was only able to pick up about 100 survivors, 20 of which were from the water, and the rest had to wait in the lifeboats until the Mount Temple came at 9:00 am, almost seven hours after the Californian.
What would happen if the Carpathia radio operator had stayed on to hear Titanic's distress calls? She was about 60 miles away, closer than the Mount Temple.
OOC: This DBWI assumes that the Californian radio operator wakes up and hears Titanic's distress calls right after the rockets are fired and arrives around 2:10 am.