Will increased precipitation in Antarctica prevent sea level rise? It has been suggested that global warming will lead to increased precipitation in parts of Antarctica. This would sequester water in the ice sheet, preventing sea level rise.

However, the slope (and thus the height and volume) of continental ice sheets is limited by ice properties. What if the ice sheet is already at its maximum slope/height/volume (is this known)? Wouldn't adding more ice just cause more flow to the sea?

According to "Ice Sheet Modeling"


  ice behaves as a deformable plastic material, which means that there
  is a critical shear stress, below which no strain (deformation or
  flow) will occur ... If the slope is too low, the basal shear stress
  will not match the critical shear stress, ... but as snow piles up,
  ... flow will begin. ... The result of this is that a glacier has an
  equilibrium profile


I am presuming that the ice sheets are already slightly above their equilibrium profile (since they are flowing). Since the profile depends on the area and shape of the base (which is shrinking due to melting around the edges), they are already holding as much ice as possible, and adding more snow to any region will just accelerate the flow. I don't know on what timescale this occurs. (I have not tried the computer models described in the paper.)
There is some scope for continuing debate because quantifying the various components of the ice/snow/water balance are fraught with difficulty, and many of the estimates have error bounds which approach the magnitude that is being measured. However, a good best estimate, subject to continuing research, is given in:Is Antarctica losing or gaining ice? 
This cites the following two graphs:

 

Clearly there are important regional differences, with East Antarctica gaining slightly, but not enough to compensate for the ice loss in west Antarctica. 

It is true that the amount of fresh snow in the Antarctic is increasing, but it still doesn't amount to much. Antarctica is still the driest continent, by far, and much more so than Australia. The controlling factor is not the amount of snow on the land, but the fate of the sea ice around the perimeter. Notwithstanding climate deniers, there is abundant evidence that the oceans' sea surface temperatures are warming, including the Southern Ocean. This reduces the seasonal extent and thickness of sea ice, which lowers the oceanic albedo, and increases near-surface heat absorbtion. It is a well-documented feedback process. Overall the warmer ocean around Antarctic destabilizes the shelf ice, thereby unlocking the glacial ice which would have been held back. So we have two opposing non-linear processes, mobilization of coastal land ice (mass loss), vs increased snowfall (mass gain). At present, and for the forseable future, the mass-loss is winning. I'm guessing this will continue to be the case because the negative feedback is very powerfull. I don't think there are any reliable forward projections about how precipitation in the Antarctic will evolve. 

(Later) In view of the comments, maybe it would be helpful to visualize the daily precipitable moisture around the world. This is available at El Dorado Weather.