If the lifeboats were able to take one trip to the Californian and had time to get most of the remaining people in them they could stay in the life boats until the Carpathia arrived.
I'll write a mini-timeline below, based on the article I linked above. I'm trying to make this basically the best case scenario.
Let's say that Captain Lord of the Californian gets notified about the first rocket spotted at 12.45, and immediately orders radio contact to be made to whichever ship launched it, and as well immediately orders preparations to be made to get the ship underway. It now takes about 30 minutes to clear the ice around the ship, as well as other necessary preparations, and then about 1 hour 10 minutes to reach the Titanic.
The time is now 2.25 a.m. The Californian would have to stop at a safe distance, not to hit the Titanic or to capsize the lifeboats in the water. Allow further 15 minutes for stopping, manning the winches and launching boats.
So at 2.40 a.m. the Californian would have her boats out and her winches manned. This would be 20 minutes after the Titanic disappered from view. The Californian's boats would start to gather survivors from the water, and the Titanic's lifeboats would move to the Californian so that the survivors could be taken to the deck.
Now, 2.40 is the time people in the water started to sink beneath because of the icy cold water - the crew of the Californian in its six lifeboats would have at most 25-30 minutes to save the people in the water. It is hard to see the six boats making more than one round trip to the site in this time, as when they get back to the Californian, all the winches would be occupied to raise the survivors in the Titanic's lifeboats on deck, stopping them to make another trip in time.
Let us also say that in this time, a handful of the Titanic's boats have been emptied and they can also return for swimmers - let's say four to six, maximum of one per winch. This gives us 10-12 boatloads of the people in the water saved by a single round trip by the Californian's six and Titanic's four to six boats before 3.10 a.m., by which most people in the cold water would be beyond help. Again optimistically, let us say each boat rescues 25 on average - and that a difficult feat under the conditions for the small crews of the boats.
So the final tally would be 250-300 people saved from the icy water - many of whom would still die from the cold before they even reach the deck of the Californian (or the Carpathia). Of course all emptied boats could try to return to the wreck site for more swimmers, but returning with survivors would be very rare and all those manning them would be very cold themselves.
And this would be how the situation would stand when the Carpathia arrives at 4 a.m. Even by the reckoning of this
very optimistic course of events, assuming nothing goes wrong in the efforts of the Californian's crew and they even are very lucky, I can't see much more than 250 more survivors than IOTL making it to the safety of the Carpathia and the Californian.
Please correct if above has glaring mistakes.