I would imagine that depends a lot on what the distance is. Release too close and you get blown up by a laser before you can release. Release too far and by the time they get there the ship will have moved away.
The missile will be smart enough to compensate for ship movements.
I don't mean the big missile, I mean the payload that InclinedPlane's strategy described - a missile shooting out a few thousand mininukes a short distance away. Such small payloads, even if we give them engines (which also makes them shine brightly to anti-missile lasers) are simply too small to outrun a ship - small engines tend to be very inefficient and slow.