The polar ice caps rely on continental masses sinking them into the earth's crust. If the ice melts quickly, did it would not occur a sudden acceleration of the sea level elevation (estimated at 37 cm by the end of this century).
The basic idea is that continental ice cap weighs down the Earth's crust. When the ice cap melts, this weight disappears and the crust rebounds, resulting in an apparent *decrease* in sea level (i.e. elevation of the land mass)--- this is called isostatic rebound.
No, because in south polar region the ice cap is mostly on land and when the ice melts, the melt water runs to the ocean thereby reducing the load on the land which causes the rebound on land. In oceans, the ice sits on top of water and melt water sits in the ocean it self, does not run away, so the weight on the ocean floor does not change.
I interpret your question as follows: if melting of the polar ice caps causes isostatic rebound of the polar region, would this rising of the land (and sea floor) also cause additional eustatic sea level rise? Something similar to this situation does occur, but it is not as simple.
The isostatic downward force of the polar ice caps causes a fore bulge in the land around it: the region around the ice caps is uplifted. This makes sea floors in the polar region shallower! When the ice cap is removed and isostatic rebound of the polar regions occurs, this fore bulge disappears at the same time. In other words, at the same time as the isostatic uplift occurs in the polar region, the land around it sinks back down. This makes the sea floors sink and it negates a part of the eustatic sea level rise caused by melting of land ice.
The situation is more complicated on a global scale, including areas outside the polar regions where there is no direct isostatic effect of the ice caps. However, there is a near-coastal isostatic effect due to the added load of extra sea water. Eustatic sea level rise effectively puts more water on flooded coastlines and the weight of this extra water presses down the land and it sinks a little, while also causing a fore-bulge effect on the near-coastal land causing a little uplift.
In the end it's the shoreline displacement that is of main interest. That is, the net effect of isostatic and eustatic processes. Unfortunately, this synergy is complicated and not the same everywhere on the globe!
Nice answer, Axel, I agree. Additionally, one has to regards the timing of the rebound, usually asthenospheric back flow takes a couple of thousands of years, in Sweden and Scandinavia it is still going on, and measured by GPS. Also, Northern Germany is affected by the decline of the forebulge as subsidence prevails.
If the (ice) pressure release on the land masses causes an average increase of 1 cm, due to the fact that the it turned to water than, the (sea)water will on the average result that the bottom of the oceans will decrease by 3/7 cm (30% land, 70% water assumed). The difference between land and sea will thus grow by 1 and 3/7 cm To make matters more complicated there is also a significant rebound effect of gravity. Due to the ice masses at Greenland and the Antarctica the sea levels around these places are significant higher. As an example, if Greenland melts and there will be a 7 meter sea level rise globally, the average sea level rise in North-west Europe (i.e Netherlands) will be only 30% of this amount (2.1 m), on the average there will be less than average rise on the northern hemisphere and more than average on the southern hemispheree. For Antarctica the opposite is true.
The answers given above pretty much cover the topic. They also make it quite clear that sea-level rise is a complicated subject, and that great care should be taken not to muddle discussions by confusing aspects like global ('eustatic') vs. regional or local ('relative') sea-level rise. As demonstrated above, these are not the same things and local relative sea level at some location may well be falling while global sea level is rising.
Because of the complexity of the subject, the study of global sea-level changes has benefited greatly from the development and application of so-called GIA (Glacial Isostatic Adjustment) models. State-of-the-art contributions in this field have been made by a.o. Dick Peltier, Kurt Lambeck, Jerry Mitrovica and Glenn Milne. Their papers are easy to find on the Internet and some of these authors have (a selection of) their publications available for download on their websites.
A good recent overview paper illustrating the effects discussed above is:
Tamisiea, M.E., and J.X. Mitrovica. 2011. The moving boundaries of sea level change: Understanding the origins of geographic variability. Oceanography 24(2):24–39, doi:10.5670/oceanog.2011.25. (I believe it is Open Access)