ACARS only transmits what it is told. It has no influence on any warning messages at all and acars does not time stamp them.
CFDS sends messages to ACARS for transmitting. CFDS also logs any ECAM warning without filtering. So for the real pilots out there can you now answer the following questions:
I have just tripped the A330 autopilot manually to off. Do I get a warning?
If yes acars will transmit it, if no acars cant transmit nothing?
Hopefully that has cleared up that one.