Not sure why you're being downvoted, as by definition, if this constant is valid for how this universe is as it is configured now then significantly changing the universe will likely result in a different constant. How you might change the universe enough to cause a variation is a bigger question. Concentrating all the stars (mass) to one place might do it. Maybe not.

The flip side of that question is the larger and generally accepted as obvious statement: a constant with value "x" determines or reflects how the universe is as of now. The duration of that "now" is likely much longer than the earths entire existence.