You mean saving the game just as you get the choice to choose your starter and turning off the game if it's not Shiny? Yeah, the rate is still the same. Even worse if the chance is split between the three choices. But I don't think that's the case.
There's your answer. Also with these games (or any, beside HG/SS), the starter preview picture will not show if it's shiny or not, so you have to actually get it and check the status screen yourself to see if it is shiny or not before soft resetting.
That chance is the same for any and every Pokemon, btw. Anyway, answered, so closed.