The barrel swap...in and of itself...won't help all that much with accuracy without also upgrading to a FF handguard/tube of some variety (of course you've probably figured that out already since that barrel won't work with your existing handguard/gas system/etc.).
At some point in time, there are diminishing returns to swapping barrels/components around versus just building or buying a complete barreled upper receiver group instead. Depending on what you have in the AR area already, you'd probably be better served to tuck the 6920 upper away for a rainy day and just buy a complete RRA Varmint A4 upper if that's the direction you want to go. Complete RRA uppers in the config you are looking at can be had for ~$600 and, as long as you do your part, should be easily sub-MOA accurate with quality ammo.
If you ultimately want just the barrel/handguard/gas system swap with your existing Colt upper...then there are tons of high quality aftermarket sources for 18-20" SS match barrels that will do the trick in addition to the RRA.
Knowing more about exactly what you want/need and your total budget for this project might help to get you in the ballpark on the "best" options to get you there.
