Since the zombie invasion reached phase 5, the number of Argent Healers decreased significantly and the zombifying time decreased to 1 min. So unless a properly geared raid with enough decursers patrol the city, it will fell to the scourge.
Since bank alts are low level, zombies can oneshot them, just like the auctioneers and bankers.
Here is a tip to survive the zombie invasion (horde only): relocate your alt to Undercity! The guards there are lvl 75 abominations. These creatures are undead therefor cannot be zombified! They quickly kill any zombie. UC is also very easy to defend for ranged DPS players, since the melee zombies has to climb long stairs to reach you while you can shoot them.
I never had any problems banking in UC, zombies came and got killed no time.