So I am ready to put a free float fore end on my 20" AR.

Right now I just have a 3-9 scope on it. It has a railed gas block that I plan on switching out to a lo-pro.

I was thinking about mounting an offset set of BUIS's at both ends of the rail once if install the full length railed free floater.

But I got to thinking...

Isn't what makes the free floated barrel more accurate with glass going to make it less accurate with irons? Once you eliminate flex in the fore end from affecting the barrel, aren't you setting up a system where the sights mounted on that free floated fore end may shift under flexion that now happens independent of the barrel?

In other words, the glass, mounted on the upper, should shoot better with the barrel now free floated. But the front sight of the BUIS set is going to shift more out there at the end if the rail than would a FSB because the tube is free floated too.

Anyone know how much this changes POI on average? For example, shooting off a rest, is it going to drop POI much?

Granted, the BUIS are secondary, and I'm not sniping at 600 yards ranges with them, but it seems to me that there might be an MOA or more shift depending on where the fore end is being stressed.

You free float a barrel. Not a rail. The rail is affixed to the barrel nut at one point, as opposed to the old-school style of attaching handguards at both the front sight and the barrel nut. This allows the barrel to remain unaffected (or float) by any movement in the handguard, such as flexing it while holding it or bracing heavily against something. Yes, flexing a rail with a front sight attached to it will cause the sight to shift and will impact your POA/POI relationship. The amount of change depends on how crappy your rail is, high end rails have little to no flex, cheap rails may have lots.

I don't think the old method was any more accurate. Flexing a barrel and handguard together does NOT mean the POA/POI stays the same. They will flex at different rates from each other, and the flex has a impact on more than just where the barrel is pointing.

This is all my humble opinion. I think you are looking for a problem that doesn't, in any practical application, exist.

this video explains exactly what you are asking about
Inside the M4 carbine
if you're very impatient the info you seek starts about HERE

But has this ever been quantified? I know that conceptually there will be a shift. But in terms of choosing a rail, for instance, how much is "lots"?

I'm not trying to be an ass, but in terms of practical use, a 1 moa shift from a crappy rail system compared to a .5 moa shift from a system costing 3x as much may be a better buy so long as it is free floating the barrel.

If all we are doing is speculating and assuming higher priced kit is performing better without testing, that seems to be taking a lot on faith.

I didn't know if any of this had ever actually been tested and quantified.

I have no idea. Crappy rails that can be deflected by hand i'd stay away from. That's really as far as I can quantify. I'd be shocked to hear that a good rail, like a Geissele, has any discernable flex. I am not equipped to measure or test this though.

how many handguards is the barrel perfectly concentric to?

Put a red dot on your scope top or offset from the upper receiver

If you are slinging up, putting downward pressure on the rail while resting it, using a bipod, etc. it would matter more than regular shooting. Holding the rail with your hand or monopoding on the magazine, especially with a sturdy rail, I wouldn't worry about it.

The Geissele + shape rails would definitely have the least amount of flex of them all IMO. I ran a stress analysis in modeling software on a MK8 13 and it showed .006" deflection where the sight is with 15 lbs of upward force on the front bottom of the rail. .006" on a 13" rail is about 1.2 MOA I believe.  I'm not sure how realistic this test was but IRL the rail combined with a heavy barrel has very little flex when pinched together. Most or all of what I notice is probably the barrel moving and not the rail.

I'm assuming you're wanting the irons for shorter range, correct?  How short?  50 yards?  Underneath that?  How much flex do you think a rail would have and how much will it mess with your POA?  My guess is not enough to matter.   Now if your're wanting it to shoot super tight groups at 200 yards, it may start to be an issue.  But even then, I'm not sure how much.  I've never seen anyone do an in depth test.  

And like someone said, it will depend on quality of the rail.  

But I've shot my recce at 100 yards with my irons on the FF rail and it performed admirably.  My eyes were probably a bigger issue than the movement. I did however take care not to put tons of pressure on the rail.  Same as if I'm shooting for groups with a NON FF barrel.

OP, I think, yes, you'll have more deflection with irons on a FF (which is not a great idea). However, most people get/use a FF for optic reasons (not to run irons). A set of BUIS is still a good idea (even deflecting sights are better than none, should your primary optic/RDS crap out).  For true irons, I'd stay with a FSB. But for optic/RDS and using buis (solely for back up), should be fine (for the intended purpose).
Or... for the win... you could go with a FF that goes around a FSB. Best of both (unless you desire a completely unobstructed view).