DOJ considers certain particular models of braces to be stocks. I don't recall which they are, but I don't believe the most popular braces are among them. Most braces are not seen as such by the DOJ (yet).
A brace can be put on a pistol, AOW, or "long gun, other", without changing the status of the weapon. If you shoulder the brace and get caught by police or DOJ (unlikely), the pistol could potentially be treated as an SBR, and the "other" would be treated as a rifle. Shouldering a brace has no effect on AOW status, since AOWs with stamps are exempt from CA SBR laws. While the ATF would surely frown upon it, CA wouldn't care about shouldering braces in that case. Braces are also not a feature for any of the four categories of firearms covered by the AWB (rifle, pistol, shotgun, and "other"), although obviously such firearms must otherwise comply with any applicable laws.