No, if the ice caps were to melt completely, the Earth would not be entirely covered by water. While the melting of the ice caps would lead to a significant rise in sea levels, it would not submerge the entire planet. The extent of the sea level rise would depend on various factors, including the amount of ice that melts and the rate at which it occurs.
The melting of the polar ice caps, including the Greenland Ice Sheet and the Antarctic Ice Sheet, would result in a substantial increase in sea levels. However, even with a complete melting of all the ice on Earth, there would still be landmasses above sea level, such as mountains and plateaus.
It is important to note that the complete melting of the ice caps is an extreme scenario that is unlikely to happen in the near future. However, the melting of these ice caps is already contributing to rising sea levels, which can have significant implications for coastal regions and low-lying areas.