No, they don’t. It is only a myth (quite popular, unfortunately) that originated due to appearance of hairs.
A razor blade cuts the hair at an angle. That is why they look thinner and lighter. The electric shaver, on the other hand, cuts them straight. Therefore, the hairs look darker and thicker when they start to regrow.
Science has proved that the method of shaving has nothing to do with hair color, density, or thickness.