VSC have ability to brake each individual wheel. OEM setup is exactly like you mention because locking a diff will make VSC behavior unpredictable. ATRAC on the other hand only manage side to side and only work on low speed so no risk of spin out of control.I thought the locking sequence is lock center, lock rear, lock front. Once the center lock is engaged, VSC is disabled, so my guess is that VSC isn't compatible with lockers.
My elocker is not wired like OEM where it would only lock in low range and with CDL locked. OEM is the safest. Mine is more fun and can be dangerous. I can accidentally lock it at any speed. It does not care low range or center diff locked or not. I experiment with it one time thinking I would need disable VSC when I engage the rear locker. This is with center diff open and high range. I was able to drift and donutbon snow almost like RWD car with no stability control. The VSC just got confused and do nothing.
Based on that experience I would almost guarantee if you put auto locker in the rear diff it would behave almost exactly the same.