...and is that 2:12:44 time for ADR DISAGREE an ACARS downlink time, or an ECAM appearance time?
It is the ECAM appearance time of NAV ADR DISAGREE, and the ACARS received time was 2:12:51. Allowing 4 secs for the up/downlink, that would give 3 secs processing between CMC and ACARS. The previous message via ACARS was received at 2:12:16, which indicates the ACARS system was probably clear.