Yes, but the drift can be calculated if your sensor suite has been reporting the target's movements correctly. However, I'd think that the slower your attack moves (eg. missiles vs. energy weapons), the more likely your foe's sensor suite is to see the attack coming and evade it.
In short, ranges of a light second or more would only be practical for energy weapons. With something like a missile the real range limit would be how much fuel it carries and how fast you can make it use it up. Once it can no longer correct its course to come after you, it's no harder to dodge than any other piece of space junk.
(10 to 16 Gs is typical for combat vessels - so I am thinking somewhere around 30 to 160Gs for missiles).
The faster it boosts the more fuel it has to carry to go a given distance under power.
This may help:
http://en.wikipedia.org/wiki/Orders_of_magnitude_%28acceleration%29