Is a varistor basically two diodes in series, with opposite polarities?
A Varistor isn't two diodes in series, it's a chaotic mesh of thousands of little diodes in all sorts of orientations.  

Courtesy of wikipedia:  


  The most common type of varistor is the metal-oxide varistor (MOV). This type contains a ceramic mass of zinc oxide grains, in a matrix of other metal oxides (such as small amounts of bismuth, cobalt, manganese) sandwiched between two metal plates (the electrodes). The boundary between each grain and its neighbour forms a diode junction, which allows current to flow in only one direction. The mass of randomly oriented grains is electrically equivalent to a network of back-to-back diode pairs, each pair in parallel with many other pairs