The chamber geometry is not the only issue! SAAMI spec pressure for the . 223 Remington is 50,000 PSI. The MIL Spec Pressure for 5. 56 NATO is 60,000 PSI.
Now, you have an accurate . 223 Remington and you rechamber to 5. 56 NATO. You have just changed your accuracy potential with larger clearances.
The WYLDE Chamber does address chamber dimension disparities. Properly done, you will have an accurate rifle.
Its not something I would do just to get cheap brass and MIL SURP ammo!
However, with a small base sizing die and brass prep. The Military brass can be used in a . 223, reloaded with the appropriate loads.
Heres a link to some good . 223 information. Have FUN! GregH
223 Rem + 223 AI Cartridge Guide
The Gun Zone -- SAAMI on 5. 56 v. . 223 Remington