Do desulfators work on batteries ?

Desulphators were considered crank devices until the late 1970's and it is true they were whether they were devices or chemicals to add to the cells.

Austin-Rover, a UK car manufacturer, had half an airfield covered with unsold cars, the majority having discharged batteries for so long they were unrecoverably sulphated. The cost of replacing those batteries as sales picked up again would have been prohibitive especially considering the amount of discount that must be given off the purchase price of the cars.

A specialist electrical company (Wilkes and Son) was commissioned to investigate and develop a machine that would recover those batteries. The company produced high quality electrical test equipment and garage workshop equipment. Their Wilkson test set was the standard in the majority of colleges in the UK.
The company developed a programmed battery charger that produced a coarse square wave output which would alternate between charge and discharge that was successful and was put into production, unfortunately it was such a large and expensive machine few were sold because the motor industry was happy selling as many replacement batteries as possible.

Typically once Wilkes had done the development and proved the technology it didn't take long for others to cash in and soon much smaller and cheaper versions were freely available.

The answer to your question is yes they do work but the success depends on the age and state of the battery to some extent and it isn't a quick process. There are other maladies a battery can suffer from other than sulphation and the true battery state wouldn't be known until your battery has been desuphated.

I suggest you invest in new batteries and a battery maintainer, either solar or mains powered which will greatly extend the life of batteries by preventing the sort of neglect that shortens battery life.