You can have a lot of fun shooting F-class to 600 yards, these matches are called midrange, matches at 800, 900, and 1,000 yards are called long range. The rig would be able to hit the paper for midrange matches without a problem but the longrange matches may be a problem if you are shooting close to sea level. The reasons are stated below.
I think you would have some difficulty reaching 1,000 yards with a 20 inch AR. The 20 inch barrel will lose enough muzzle velocity that you will probably be subsonic before reaching the target. There are people shooting 20 inch bolt guns to 1,000 yards but the loads they are using are quite stout and your AR may not be able to handle those loads. All of the above is bunk if you are shooting at elevations well above sea level.
The way to 1,000 yards for you, if interested, might be to buy some 155 Lapua Scenars as they have a BC that is very close to the 175 g Sierra Match King and can be pushed faster. If it were a bolt gun I would also say get a 20 MOA scope base, but that does not work for an AR without significant gunsmithing, I believe you can get rings that will work in place of the 20 MOA base. Without the 20 MOA base or rings your scope probably does not have enough elevation to get to 1,000.
I know I just dumped a fair amount of info on you and you may be confused, maybe you should ignore it all and just start shooting midrange and if you have fun then think about reaching 1,000 yards. You can have a lot of fun and learn some sound skills shooting midrange F-class.
wade
For starters I'd say worry more about competing against yourself, trying to do better each time you go out and not make the same mistakes too often if possible.