Yes, indeed, it certainly works, and is a useful economy measure.
There are no major disadvantages provided you don't go mad. Some varieties have nearly all the eyes at one end so try to ensure both bits have a few. It is worth allowing a period for the cut surface to dry out in order to reduce the risk of rot and other diseases. Also the seed potato is the source of nutrition in the early stages of growth - make them too small and you will get a weak plant and low yield.
How small is too small though? I've seen various recommendations on line. No lower than about 2oz seems a popular choice.