If they had turned sooner, they would have missed it. If they had turned later, they would have hit it head-on, crumpled the first few bulkheads, but survived because the water wouldn't have been able to reach back further.
Which was the plan, of course, because it wasn't the Titanic that sank - it was the Olympic, that had been name-swapped for insurance purposes after a collision. That's why they coaxed the captain out of retirement to sleep through a full-speed order through a known ice field in the middle of the night.
They just didn't count on a side-swipe.