Theoretically.. yes! Given the prevailing conditions during the early hours of April 15; it would most certainly have been possible for every living soul to have been transferred from Titanic to another ship. However... and it's a big 'however'...it would depend entirely on the type of rescue ship. Lets suppose it was in fact Carpathia
or a ship like her.
In some photographs of survivors I have seen.. it shows side-doors in Carpathia
's hull. These are very large water tight double door entries for gangways.
To create a rescue scene.. we have to change a few things.
First: Carpathia is the ship approaching Titanic at or near midnight. For the previous 20 minutes; both ships have been in contact and between them, have designed a passenger transfer plan. The plan consists of the rescue ship approaching Titanic and stopping close-to her...say about 200 yards away.
As Carpathia approaches Titanic, she swings-out all her own lifeboats and fully crews as as many as possible. She also opens her side doors ready to receive survivors.
All her own passengers are awakend and moved well clear of the entries but distributed evenly over the ship. In the meantime; The Titanic boats are made ready as normal. However, the boats are each pre-loaded with about 40 passengers.. all have been informed of the plan! The remainder are arranged in groups to facilitate loading of lifeboats in an orderly manner.
As soon as Carpathia is in position and stopped,she launches her empty lifeboats. These head across the 200 yard gap to Titanic. In the meantime, Titanic's first wave of survivors is in the water and starts heading for Carpathia.
On the way, they are passed by Carpathia's boats heading for Titanic's gangway doors.
The boats from each ship arrive at their respective destinations about the same time. The first load of survivors is unloaded onto Carpathia and Titanic's empty boats head back. At the same time, the boats from Carpathia are loaded with Titanic survivors and head back to Carpathia. Two trips of Titanic's boats would transfer 1800 souls leaving 428 people to be transferred by Carpathia's boats.
An undermanned ship's lifeboat would make about 2 knots in conditions of flat calm... that's 101 feet a minute, meaning it would take about 6 minutes to make the trip between ships. Each lifeboat would be unloaded as it arrived at Carpathia. This would take about 5 minutes. So in theory; a sort of conveyor system could be quickly set up. Boat leaves Titanic and is back alongside her for more passengers about 20 minutes later. They could also have rigged an endless line between the two ships and used Carpathia's winches to pull boat-loads of people across the intervening space. Empty boats being attached to it for the return journey. Lots to play with here!