Yep... though in that case, the endgame would've been different. It was supposed to be (if I recall correctly - it's been many years) a downbeat ending along the lines of "Bradshaw and Sparrow lived happily ever after, until the Kilrathi blew up the Earth and hunted down all humans".
Ultimately, we just didn't see the point putting so much effort into a dead-end path that distracts from the rest of the game, and also, we didn't like the idea of someone trying out this path first, and learning about Sparrow - the reveal on the normal path would lose much of its impact then.
(plus, the implicit idea that Bradshaw followed Sparrow only to have her leave him behind for Confed is just too wonderful to refuse)