
No way, that just isn’t realistic at all. Let me outline exactly why this idea would have gotten you killed even quicker than staying in the water.
First, the water was about 28ºF -2ºC that night. At those temperatures, you’d have maybe 15-20 minutes before hypothermia knocks you out.
Swimming actively? Well, you cut that time in half because with movement, one loses heat quicker in water.
The iceberg wasn’t merely floating abreast of the ship.
By all survivor accounts, and the ship’s log besides, it was a quarter-mile away by the time anyone began going into the water.
That is a long way to swim in normal conditions. In icy water, in all those clothes? Impossible.
But say you did make it onto the iceberg; now you are faced with a wall of ice that’s just one huge, smooth, cold cliff.
Most bergs in that part of the world break the water by about 50-100 feet. No handholds, no ledges, just smooth, wet ice.
Your hands would get numb and useless from the swim; your clothes would be frozen solid.
And besides, icebergs always shift and roll with their melting. Even if you were able to climb up-you can’t-you’d run the risk of it suddenly flipping over, as they are wont to do.

Those who boarded the lifeboats, or remaining afloat close enough to the ship well enough to make it onto actual floating debris pieces or a few collapsible lifeboats were the only survivors of that night.
Of the ones that swam away from the immediate vicinity? None survived.
The water was cold, about 28F. Like a little below freezing cold. Your arms would be like lead weights after 50 feet. Your clothes are soaked with ocean water, creating more weight for you to swim with.
That iceberg is pretty far away. No matter where you jump from, it’s a long drop to the water, which is very hard on impact. After regaining your senses (if you do), you have to work around the ship and avoid the suction created by a massive sinking vessel. That’s a long swim, alone.
But you are a stud swimmer with medals from high school swimming competitions. You believe you can make the swim. After all, it is only a mile or two away by some estimates. The propellers were still steaming at 21 knots immediately after impact and then momentum. Nothing stops fast on water.
Still think you can swim a mile or more in 28 degree water to get to the iceberg? If you say yes, I won’t believe you. You’ll freeze to death or go unconscious and drown.
Even if you made the iceberg, you have to climb up ice with no tools, no grip, no nothing. And the iceberg is made of …. ICE. Your hands will hate you for the swim and give out when you try to grab the ice. And even if by some miracle, you make the swim, climb the iceberg, then what? No way to get warm, its pitch black, and you are soaking wet.
You will die before getting close.