This hypothetical is getting into "if my granny had wheels she'd be a wagon" territory. I interpreted the original comment as if the Sun, with its current mass

This hypothetical is getting into "if my granny had wheels she'd be a wagon" territory. I interpreted the original comment as if the Sun, with its current mass, had an iron core. A star with the mass of the Sun cannot have produced iron, so it would have had to have formed with an iron core. This is certainly ruled out by other data, of course.