The cell would burst.
In distilled water, the water potential is the highest, which is higher than the cell cytoplasm. So in this case, there's a concentration gradient, and water molecules will start to flow from the distilled water in the cell because of osmosis. Osmosis is always the flow of water molecules from a region of higher water potential to a region of lower water potential, through a semi permeable membrane, aka the red blood cell membrane in this case.
This leads to the large amount of water gained by the red blood cell. The cell membrane cannot hold all water and therefore the cell bursts.