No. Cell-plasmolysis is not necessarily fatal for the cell. Plant cells normally recover from this condition when water is available. (But cell death can take place in excessive or prolonged lack of water).
It is an incomplete truth that during plasmolysis, plant cells get detached from the cell wall. Actually the plasmodesmatal connections remain there and a portion of the cortical (outermost)-layer of cytoplasm, mainly containing "cortical endoplasmic reticulum", a group of endoplasmic reticulum spanning close to the cell wall; remains there.
Now, when plasmolysis take place, the cell-membrane shifts apart from the cell wall; but at the place in-between, there forms fine cytoplasmic threads called Hechtian strands. So the connection is retained. (As well at some portion of cell-wall, the bulk protoplast remain touched there)
Here are photos showing hechtian strand; taken from the book Plant Cell Biology- structure and function, by Gunning and Steer, Jones and Bartlett publishers, Copyright 1996;
Image-1 (Book image 16-C)
Hechtian strands of stretched plasma membrane extended from the plasmolysed protoplast to the cell wall (K. Hecht , 1912, was the first to study them in detail). This confocal micrograph shows strands in a 16 μm- deep zone. Some strands extend from plasmodesmata (arrows), where the membrane passes through the cell wall, butmany attached to other sites. in 1931 another early investigator J. Plowe, pushed plasmolysed protoplast along inside their cell walls, observing that existing strands stretched and broke, and that new strands could form. In today's terminology we would say that new strands arise when freebinding sites on the plasma membrane contact and bind their ligands in the cell wall.
Plant Cell Biology- structure and function, by Gunning and Steer, Jones and Bartlett publishers, Copyright 1996
Update: An interesting information; there is one method of plant protoplast isolation without enzymic digestion of wall; which uses plasmolysis. Since the protoplast(and cell membrane) get shifted from part of cell wall; it becomes easy to rupture the wall without rupturing the cell-membrane. (Discussed in this website). The protoplast remains alive after plasmolysis otherwise we won't be able to use this method for protoplast culture, cell fusion etc.