Barrel length doesn't directly affect accuracy per se. However you may find it harder to shoot a 16.5" rifle as well as a 24" rifle for a few different reasons.
"Service rifle" barrels are longer, but that's just because NRA rules arbitrarily dictate 20" ARs, 22" M14/M1As, and 24" Garands as "Service Rifles" as opposed to "Match Rifles" for highpower matches. Arguably, the 20" AR is the most accurate rifle in the bunch, but that doesn't have much to do with the 20" barrel length.
Lighter guns have heavier recoil, which makes learning to shoot accurately more difficult. Long, heavy barrels soak up a lot of recoil and make it easier to develop good technique.
Longer sight radius when using iron sights can make it easier to shoot more accurately, which is easier to do with a longer barrel. Scopes don't care how long the barrel is.
A rifle with a long, heavy barrel wobbles slower than a short rifle, making it a little easier to shoot accurately, especially from unsupported positions.
Keeping the bullet above Mach 1.2 before it gets to your target results in better accuracy. To get a .308 to stay that fast to 1000 yards requires a crazy long Palma rifle barrel and slow powders to really drive the bullet fast when it leaves the barrel. Forget that sort of performance out of a 16.5" rifle. 600 to 800 yards should be within reach.
Barrel quality plays a MUCH bigger role in accuracy than length, and I don't know how good your barrel is. It might be awesome, or it might be a dog. Likely it falls somewhere in between.
The biggest factor in accuracy is your shooting technique. Shooters with good technique can compensate for some pretty substandard equipment.
The next biggest factor is probably the quality of the trigger...bad triggers are really hard to shoot accurately. Next comes the rifle itself: barrel quality, uniform barrel crown, stock fit/bedding, how the rifle fits you, etc. Next would be finding a load your rifle likes. Then optics. Then maybe barrel length.
I'd say find some federal match .308 ammo and see what you and your rifle can do with that. Try a bunch of other brands and see if some are good and some are bad, and keep good notes. Don't do this with 3 shot groups. 5 or 10 shot groups will give you much better info. When you find something your rifle likes, try to replicate that with your handloads as a starting point for load development. Right now is a terrible time to start reloading because there aren't a whole lot of components to be found for .308, but that will probably get better in a few months.
Good luck!
-J.