I've tried to research this online and looked through my textbooks as well. This is something that has been on my mind for a bit. Will it just mean that the organism is more simple? Or would it mean they are less efficient? I'm not sure.
If we consider a mammalian organism, it would eventually die, and one can presume that it would not take too long. In mammals, a lot of tissues are primarily constituted by specialized cells that cannot divide. Some of these cells have a tremendous lifetime (e.g. neurons), but others have a much shorter lifetime (e.g. erythrocytes). In tissues that are composed of the latter type of cells, certain stem cells are actively differentiating in order to maintain an adequate number of such cells in the organism. If such differentiation suddenly stopped, the concentration of such cells would progressively drop as time goes by, until the functions carried out by such cells are not executed. At this point, without these functions (e.g. oxygen transport carried out by erythrocytes), where some are essential, the organism would quickly die.
Then you'd have lumps of unspecialized stem cells. Differentiation means that most of the genome has been turned off and only a subset of the genes is active. Makes IMHO sense in the light that different cells make use of the same signalling pathways downstream of different receptors to elicit cell type specific responses.