The fine structure constant may not have the same value throughout the universe, but I'm still curious if its a measurement error. Changing it by much would prevent the synthesis of carbon in stars. But are you suggesting a different value would allow some other atom to take on properties as useful as carbon? If so I would like to read more about it.
Regardless, if there is a gradient, any meaningful change in the fine structure constant beyond the range at which we could observe anything in the universe, so it still makes sense to only assume carbon-based life.
This assumes the fine structure constant has the same value throughout the entire Universe for all time. Tentative results from recent observations suggest it could increase in one direction and decrease in the other along one of the spatial dimensions of the Universe.