Thank you for your question. The simple answer is no. The whole world will never be underwater. But our coastlines would be very different.
If all the ice covering Antarctica, Greenland, and in mountain glaciers around the world were to melt, sea level would rise about 70 meters (230 feet). The ocean would cover all the coastal cities. And land area would shrink significantly. But many cities, such as Denver, would survive.
However, all the ice is not going to melt. The Antarctic ice cap, where most of the ice exists, has survived much warmer times.
The concern is that portions of the Greenland and West Antarctic ice caps may disappear. We do not know how much or how quickly this could happen, because we do not know exactly how it will happen.
That's because the ice doesn't just melt. Ice actually flows down valleys like rivers of water. The problem is that we do not completely understand the factors that control how rapidly the ice flows and thus enters the ocean.
One way to approach the problem of not understanding the process is to study how sea level changed in the past. Earth is nearly as warm now as it was during the last interglacial period, about 125,000 years ago. At that time, sea level was 4 to 6 meters (13-20 feet) higher. It seems that this higher sea level was due to the melting Greenland and West Antarctic ice caps.
Perhaps a similar sea level rise is our future. We don't know. We also don't know how rapidly sea level could rise. Will a 4-meter (13-foot) increase take 200, 500, or even 1,000 years? This is a question that a number of scientists are now trying to answer by studying how ice moves.