Pg 10 of the Rulebook:
"Note, you must roll for all attacks declared on a ship before rolling on the Damage Table..."
So, yes, you have to roll all of your attacks. Period.
I would say, though, that some leeway should be granted if you get it to -17 damage before you have finished rolling. It's going to explode regardless at that point.
On the other hand, as soon as you have rolled on the Damage Table for a ship, you can't shoot at it for the rest of the game. So no making Adrift ships explode.
(I would actually houserule that one out. If it's still on the table, you should be able to keep firing at it if you want. Nothing like using a dead hulk as a weapon...)