Would a red blood cell behave in a similar way to a cell that does not allow solutes to pass through the cell membrane?

No, a red blood cell does allow solutes to pass through its cell membrane. The cell membrane of red blood cells is selectively permeable, allowing certain solutes like oxygen and carbon dioxide to diffuse across it. However, the membrane of a red blood cell does not allow larger molecules like proteins to pass through. So, it is not similar to a cell that does not allow solutes to pass through its membrane at all.