Lets say water is rushing in at 250 gallons a minute, at approx. 8# per gallon that would be 1 ton a minute. As the ship gets deeper water comes in faster. Also there is one other factor, and that is boyancy. As a ship takes on water, and loses boyancy, its not just adding weight to one side of the scale, its knocking weight off the other side.
Plus, eventually so much water was in the ship that the ship ripped in half.
The calculation is fun but you need a couple more zeros on the flow rate . The iceberg split was over 100 feet long and busted rivets went much farther. To be meaningful you would have to step up to more like 25,000 GPM flood rate. But there's plenty of evidence the whole bunch stood around like dunces. A few engineering students might have helped. My thot over the years has been that getting at least some people onto the berg and rigging extra floatation should have helped. But now everyone would just be shooting video hoping for the best!