I'm going to be setting up my Stag Arms A4'gery as a bit of a trainer with a spike's converter. For 0-200 yards how close with the point of impact be for these two rounds? Is there a method that I could use best to zero for them both? I realize that 200 yards may be pushing it for the 22 to match the 223. Suggestions? Thanks.

tag

At 50 feet, my .22 conversion (Colt, but that probably makes no difference) hits about 2.3" low, the 5.56 would be about 1.6" low at that distance.  So that's a .7" (3/4") difference.  
I expect the difference would be greater at longer ranges because the .22 will be dropping faster.
EDITED TO ADD:
These numbers are with a Leupold VariX III 1.5 x 5 scope in a LaRue QD mount, not iron sights.  But the scope is the same height above the bore as irons, so the numbers should still be valid.
Groups at 50 feet are about 3/4" wide, 1 1/8" high; fired by leaning over a booth shelf onto my gear bag.  A good rest would probably eliminate the excess vertical dispersion.

Ok, thats pretty negligible in my mind. Good enough for hunting rabbits under 100 yards or putting holes in paper.
Thanks

Its very easy to dial the rear A-2 sight up to 4 or 500 yard mark it you want it to shoot point of aim at 25  50 or 100 yards.  If you use a 50 yard battle zero I think you'll be surprised how close the 22 rimfire hits to the 223/5.56 out to 50 yards.  At 100 yards the HV 22 lr will probably drop 4 to 6 inches at 100 yards with the 50 yard zero.  The box of Federal 36 grain Hollow point value pack 550 box sold at Walmart shows 5.6" drop at 100 yards.  Shooting at a steel bowling pin off hand at 100 yards if I aim at the head of the pin I hit it in the body with 22 lr in my 16" AR sight at 50 yards.  Either way its fun and very good practice for CQB training and plinking.  With a 100 yard 5.56 zero I don't notice quite as much drop with the rimfire at 100 yards.  The windage has always been pretty close using a conversion kit on my 1:9 twist barrels.  Results can vary but that's part of the fun finding out what works with your rifle/carbine.

Awesome thanks for the info. The other part of the equation is that I wish to purchase some glass to use this rifle as a trainer for a 16" 6.5mm Grendel I hope to buy soon. My thoughts are that if I get a 1-4x scope for the .22 to shoot 50-200 yards and get a 3-9x or a 2.4-10x scope for the grendel for shooting 100-600 yards and try to pick scopes with similar reticles. Thoughts?

I think you have a plan.  A dedicated upper in 22 lr with 1:16 in twist barrel will give more consistent groups than a 22 lr conversion in a 1:9 or 1:7 twist 5.56 barrel.  If your going to use a dedicated upper I think the 22 lr is great training aid.  Believe me you have to be able to read the wind when shooting a 22 rimfire from 100 to 200 yards in the same way when your shooting that big 6.5 out to 600 yards or more.  Besides if you have the same trigger and stock basically your mastering the system.  I have shot many thousands of 22 lr since being issued a patrol rifle.  The 22 LR in the AR has made me a lot better shot and improved my confidence in a way I could never been able to do if I had to shoot 5.56.  Besides I personally get the same enjoyment out of the AR platform whether shooting rimfire or centerfire.   There is a certain amount of satisfaction for me to shoot a steel bowling pin shaped target off hand at 100 plus yards with a 22 AR and hit it almost every time.  Its your money if you can afford it try it.  Usually if you don't like what you bought you can resell the stuff for close to what you paid for it.

ooops. double post

When I had a conversion I sighted my .556 at 50 yards. The .22 hit within a couple inches of that. I left it alone.

Ok, I have a slightly new concern. I want to go to a Appleseed shoot in April. Obviously I want to be using the .22lr at least for the first day. As a possibility I may want to shoot .223 the second day. Do I buy a seperate rear BUIS to have them both zero'ed properly? What are your suggestions? I also think I read somewhere that some one had a sight that the simply elevated up to the 400 mark when they shot .22lr to make up for the difference. Think that would work?