The extra load on an alternator by a battery with a shorted/dead cell is minimal, If the other 5 cells are still within 20% of being at full charge, but the one dead cell will discharge them. It is a matter of time of how long the dead cell is allowed to suck down the other 5 cells. Any well depleted battery can ask for huge charging currents from the available charging source.
The extra stress on the other 5 still functioning cells is greater when the alternator is holding the battery in the mid 14's. They will heat up and offgass significantly more than a 12v healthy battery with 6 functioning cells.
If you do drive the vehicle to the battery store, I would open the hood, feel how hot the battery is, and sniff for any sulfur smells.
If the battery is hot and stinky, I'd wait a while before disconnecting the cables and possibly causing a spark.
The 5 still good cells will have been bubbling vigorously and the tops of the cells filled with oxygen and hydrogen still trying to escape.
The shorted cell could be bubbling even when no charging current is applied to the battery.
A battery with a shorted cell can be dangerous. I'd remove it from the vehicle, rather than make it more dangerous by force feeding the 5 other cells at what will be rather extreme voltages for an hour drive to the battery store.
The chances of explosion are not profound, but the consequences should it happen can certainly be.
If you make it there, and they install the battery for you, inform the the installer the shorted cell before they open your hood.