No, it was not able to be saved after it hit the iceberg, absent a miracle like a floating dry dock or full repair facility dropping in out of the blue.

There were a couple of things that doomed the Titanic. The first, of course, is that its watertight compartments weren't truly watertight -- they did not extend up to the level of the top decks, because doing so would have meant that the bulkheads between compartments would have disaccommodated passengers trying to pass along the length of the ship's upper decks. This is what allowed them to fill and spill over, like what you see in any bog-standard animation of the sinking.

Second, the nature of the damage to the side of the Titanic would have overwhelmed the ship's defenses against flooding in any case. The ship was engineered such that any two watertight compartments could flood and it would stay afloat -- the designers of the ship imagined a collision occurring at the junction of two compartments to be a worst-case scenario. (In theory, the four foremost compartments could flood, but the narrowness of the forward hull meant that flooding in those compartments would not result in the ship capsizing/sinking.) In fact, the iceberg opened holes in five of the ship's watertight compartments, though not large ones -- the whole area open to the sea is only estimated to be about 12 square feet. The ship's pumps were not capable of dewatering it faster than the water was flooding in. Thomas Andrews, the builder of the ship, was actually aboard with a party of engineers; he estimated that at the rate of flooding, the ship would sink in about two hours. (She lasted 2 hours 40 minutes after the collision.)