There are two ways that the insert could apply backthrust to the breech. Gas pressure on the muzzle end of the adapter (classic floating chamber application), and backthrust resulting from the adhesion under pressure of the cartridge case to the adapter. These would probably not be substantial.
If the diameter of the inner base of a .30-06 case were, say, .400", its area would be 0.126 square inches. A=pi times square of the radius. If maximum pressure is 45,000psi, then 0.126 times 45,000 equals 5670 lbs applied.
A .223 might have an internal area of .08 square inches (.16x.16x3.14159). With a pressure of 50,000 lbs, backthrust of 4,000lbs.
A steel adapter should be able to contain the hoop stresses generated by a .223. Backthrust should be less than that generated by the original cartridge.
Combined headspace of the adapter and cartridge should also be considered. If loose, a ruptured .223 case head would be most undesireable.
Firing pin fit and diameter are also an issue. Blown primers can result from a large diameter firing pin coupled with a sloppy fit.