If you're talking about a bolt/chamber conversion unit that uses the AR barrel, not a dedicated .22LR barrel, you can expect about "plinking grade" accuracy.
I have a GI M261 unti and have run it in three different 1:12 barrels and one 1:9 5.56/.223 barrels. To put it in numbers, if you can find some kind of ammo that will stay inside one inch at 25 yards in your gun, you will be doing pretty well. If you can consistently beat 3/4" at 25 you are doing VERY well. Anything better than these numbers is pure gravy.
By comparison, I have few .22 rifles that won't easily stay inside a half-inch at 25, including both my 10/22s (factory stock mechanicals).