Can the terminal voltage of a lead acid battery be reversed?
Actually it is possible, but this will ruin the battery irreversibly. The trick is that the fully discharged Pb-acid battery has both electrodes the same composition \$PbSO_4\$. When the battery is charged, the negative plate contains pure \$Pb\$ and the positive - \$PbO_2\$ . 

This way, if you fully discharge the battery, it can be charged in reverse way. The big problem here is that the positive and negative electrodes have different design, because of their destination. Even the full discharge of the battery is pretty destructive and reverse charge will cause fast plates degradation and in result big decreasing of the capacity and the possibly little bit later internal short circuits in some of the cells.