Yes you can connect two 6 volt batteries in series. Whether the treatment is successful depends on why the battery isn't holding a charge. If it's due to plate sulfation, the charger may be able to reform it back into active plate material.
If you have a shorted cell, it won't.
If you have a hydrometer, before you charge the battery see if you get equal specific gravity readings on each cell. If two cells test good while the third is near zero, you have a shorted cell.
Another way to find a shorted cell is with a voltmeter. Put one voltmeter probe on the (-) battery terminal, then dip the other into the electrolyte of each cell. Don't touch the plates, just the liquid electrolyte.
Good cells will increase the voltage by about 2 volts each. i.e. the first cell will read 2 volts, the second 4 volts, the third 6 volts.
If you have a cell that doesn't contribute an increase in voltage, you have a shorted cell - probably due to plate structure flaking off and accumulating in the bottom until it shorts out the cell.