Universal only if the bits used on the A and B outputs are "non-retentive" through a power-cycle, or operating mode change.
On Allen-Bradley PLCs, a "pre-scan" automatically resets all non-retentive outputs, resets non-retentive timers, etc.
This must happen in order for A to be turned on on the first "proper" scan following the pre-scan.
On some makes of PLCs, you have a choice of retentive bit memory, and non-retentive bit memory. Of course you would need non-retentive memory for A and B.
If all of your internal bits are retentive, then you would definitely need a "first-scan" status bit from the processor, and there'd be no need to "roll-your-own".