Osmosis envolves automatic physical reactions at a molecular level, and therefore, it does not cosume energy from the cell. If the cells are dead (not producing energy anymore) but if they are relatively fresh and if they are not dry (and 80% of a potatoe is water), I suppose osmosis continues to occur. The passage of water molecules though the cell membrane(osmosis) occurs directly due to channel proteins that cross that membrane. If a cell contains water, there is no obvious reason why it should not keep its structure. So, if the structure is intact, as long as there is not a isotonic balance, osmosis should continue happening, to achieve that same balance (in most plant cells, such as potato cells).
Isotonic balance is when the density (of solute) outside and inside the cell is the same. Plant cells tend to achieve this. To achieve this, the cells loses or gets water (osmosis), and loses or gets solute (difusion). The movements of matter occur by phsical priciples that require mixing intracellular and extracellulr solutions to achieve balance.
*I assume that you talking about an experiment with a microscope...
Thank you.