The basic thing to understand, is that your standard flasher functions by application of current. As current flows through the resistive bi-metal strip in the flasher, the strip heats up and curls. When it curls, it breaks contact and current stops. Hence it then cools down, and un curls. Contact closes and cycle repeats. The reason that LEDs don't work with the old style blinker pots is that the LEDs don't pull much current. That is what the add on resistors accomplish.

I don't know how the electronic flasher operates, but I would suspect it is driven by a 555 timer, or perhaps an RC circuit for pulse width, and transistor control. Hence it would be current independent. Assuming you don't overload it, of course.