Not exactly. The ACARS can be programmed to send information on a wide variety of parameters on que, such as at a particular radar altitude, change in configuration (slats, flaps, gear) or at a particular time interval to transmit engine data.
For example ACARS is how airlines monitor their crews for stable approaches (speed, configuration, vertical velocity, deck angle, g-loading, etc.), triggering a message with various parameters at 500, 1000, or 1500 feet on final (examples). But the ACARS doesn't transmit continuously since that would cost too much for all the extra messaging (especially overwater with SATCOM as primary).
This is what strikes me as strange: if indeed RR and Boeing got routine ACARS messages on engine performance hours later, then surely the airline also got numerous ACARS messages that were automatically sent. And if they did, then why are they so secretive about the content of them, or even their existence?
There is NO verification that any data was sent after 1:07 am so quit speculating. Your example of programability is for one of the crucial data sets that are looked at... take off, climb, approach, landing.
It is NOT a real time black box mime