This is greatly dependent on the cell line you are dealing with. Some cells are more sensitive to changes in culture media and other you will find them hard to kill no mater how bad you treat them. One thing to keep in mind is that you might not see a direct effect on cell viability but there is a great chance that your cells have been altered. As Sebastian said, your cells will react to the hypertonic solution and might adjust themselves to survive.
1 M buffer (2000 mOsm, normal is ~300 mOsm) will definitely raise the osmotic pressure of your medium enough to shrink your cells into non-existence. It also achieves nothing, the medium will have run out of nutrients long before the acid level has increased enough to warrant such high buffer concentrations.