Because the reversed battery is no longer formatted correctly, it will only work to a limited degree. The fact of the matter is, a lead acid battery cannot reverse its own polarity without an external stimulus. It is just not possible. Guilty As Charged Blog Post touching on the battery myth of reverse polarity.
With a lead-acid battery it will reverse charge, but you may compromise the battery life and efficiency. I know the two poles are different materials (lead anode and a lead-oxide cathode). So, the chemical process is going to be slightly different and you may also overheat the battery solution is charged too fast. Exploding H2SO4 is very bad stuff.
One thing you could do, but this would ultimately lead to the destruction of the battery plates inside, is to use the battery in reverse. The battery plates are not meant to be charged in reverse, so continuous cycles of charging and discharging will destroy them, but you could maybe get a few cycles out of it.
If controlled-current reverse charge is done long enough, the chemistry of the reactions will cause the polarity of the battery to also reverse as the lead compositions coating the plates reverses.
You could technically charge it up, negatively, and continue to use it, but your plates are designed with the positive plates being lead dioxide, and the negative being composed of a sponge lead, which would now be reversed. Because the reversed battery is no longer formatted correctly, it will only work to a limited degree.
It may discharge the battery with spark or permanently damage the battery. In other words, the reverse polarity battery connection, the DC supply would drag electrons from the negative terminal of the battery and push them at the positive terminal. This would gradually discharge the battery same like in case of a capacitor.