Yes it does. The system effectively notionally assigns seats when the flight comes under airport control 48 hours before the flight. Remember that many people on connecting itineraries may also be checking from around that time as their check in opens 24 hours before their first flight (rather than before each flight).

In recent months, things have become all the weirder with BA using both old and new versions of the interface so in some cases when my assigned seat was unavailable for any reason (e.g. expected to be faulty or curtain change), refreshing the app would jump back and forth between my assigned seat and another (what the system had assigned me as a fall back option).