I would think that the captain would have. After all, he went below not long after the collision and assessed the damaged for himself. It stands to reason that he, Hutchenson, Wilde, and Boxhall would have, or did, realize the seriousness of the situation early on.
However, I would have to postulate whether or not the loading of the boats would have been conducted in as organized fashion that it had. Would the boats have been uncovered and loaded into the davits when they had? Would the rule "women and children first" have been so stringent? Would more people have died? (it is my contention that Andrews had a direct effect over the quantity of those saved). True, there were certain protocols that seamen followed, as there are now, and that would stand whether Andrews had been on board or not, but it seemed that his role had a major influence over how things were done that night. His input, it seems to me, was one of those conditions that had sent everything into motion onboard.
How would it have been different? That's another question altogether. I guess we'll never know for sure, only that, considering his influence in the crew's reaction to the collision, things would have likely been different.
I could ask the same thing regarding Ismay. Would things have been different if he hadn't been on board? If so, how?...
And if Gracie or Beesley hadn't been onboard, we wouldn't have had the detailed, captivating accounts that we now have. Everyone played a role; each person's experience was significant in some way.
Interesting question, Paul.