How big is the gap between the brick and sheathing? If it's 2" or more filling the gap would give you a reasonable R value even without filling the stud bays and would be relatively safe for the sheathing. If it's an inch or less, the insulating value is miniscule, and there is increased moisture risk to the sheathing.
The space between the masonry and the sheathing is necessary to protect the sheathing from moisture drives coming from the exterior. It works best if it's vented to the exterior at both top and bottom. The vents don't need to be huge to work, weep holes every 3- bricks or so at the bottom and corresponding slots cut into the vertical mortar between bricks every few bricks on the top layer allows enough convection to purge high moisture conditions. These conditions typically happen in summer. Brick is porous and will absorb & store a good amount of rain & dew. When dew or rain-wetted brick gets heated in the sun the moisture is driven off rapidly resulting in VERY high humidity levels for a few hours at a time. But as long as the sun-heated very humid air in the cavity space is allowed to convect to the outside pulling in drier outdoor air, very little of that moisture ends up in the sheathing.
When you fill the gap with non-expanding injection foam there is no convective purging taking place, but the foam itself is modestly vapor retardent (about 15 perms @ 1", about 8 perms @ 2"). The 15# felt commonly used on the sheathing in those cavities is more vapor retardent than the non-expanding injection foam, but at 2" or more the foam is at least helping, whereas at 1" or less it's permeance is too high to have any protective aspect at all.
In a Tulsa climate the resulting higher average moisture content in the poses absolutely no risk to the brick, but in much colder places such as Winnepeg or Fargo, closing up the gap with foam would risk freeze/thaw spalling on the exterior face of the brick.
The other significant question to answer before filling the gap with foam is how the flashing on the windows & doors are set up to drain. If (as is common) the flashing is using the felt on the exterior of the sheathing as the drain plane, filling the gap with foam could result in higher moisture content in the window & door framing with rot potential, since bulk-water incursions would take an order of magnitude longer to dry.
In general the safest thing to do is to insulate the stud-bays, and leave the masonry cavity alone. (If the cavity is not already vented, drilling in vents & weep holes on the top & bottom courses is worth it.)