Why not add it outside of the sheathing and under the cladding?
In short if you are compressing the fiberglass, you are diminishing its ability to work properly. Fiberglass gets most of its insulative properties from the air pockets created in-between the fibers. By compressing these you are eliminating those air pockets & reducing it's effectiveness.
Ahhh but how about those high density batts - well in order to get that .5 to R1 increase per inch they actually have to double the amount of fibers used. In order to raise it again they have to double the fibers again.
So let's say you compress an R 13 batt in half. While your R Value per inch theoretically goes up, the overall R Value of the assembly has dropped as it is no longer as thick.
Your best bet is with the first question I asked - why not put the foam board outside of the cavity? You will still need to air seal, but you will eliminate a ton of other issues. Now if you are not removing the exterior siding and doing this from inside, then put the foam boards in and seal (assuming you have no water issues) - then either dense pack or wet spray those cavities with FG or cellulose.