Tell me you don't know anything about electric guitars without telling me you don't know anything about electric guitars.
Wood has a great deal with how an electric guitar sounds. Maple-topped guitars are brighter, as are guitars with maple necks.
Leo Fender used ash and alder because they were readily available and sounded good. Pine electrics are light but have a different sound. Solid maple electric guitars are extremely heavy.
Unfortunately, a lot of "old-growth" hardwoods are scarcer than they used to be and we're seeing in increase in alternative woods from Asia such as basswood. Brazilian rosewood and ebony from Madagascar used for fingerboards is now much harder to come by and can run afoul of CITES laws (what Obama pummeled Gibson over). We're even seeing in increase of fake wood like Richlite (super compressed cardboard + epoxy resin) enter the manufacturing process.
Type of wood used in electric guitar manufacturing contributes to tone, sustain, durability, and weight and matters a great deal.
Sure it does. However the tone control does a heck of a lot more. Or a programmable amp will make it sound any way you like.