Hazelnuts39 asks how far off satellite time might be from aircraft time or ground time.
The satellite would be very close to ground time. The satellite is constantly in touch with several ground stations which can provide it with corrected time certainly within milliseconds accuracy and probably much better. So I think we can stipulate that on terms of seconds the satellite is right on the mark with the ground stations.
Suppose the ACARS protocol does not require precise timing on the aircraft and as such can wander considerably. (I doubt this is the case.) A cheap crystal oscillator without any fancy temperature compensation is cut to about 50 ppm accuracy and wanders 25ppm to 50ppm over various military temperature ranges. Let's suppose it sits 100ppm, 0.01%, in error for an entire 12 hour (43200 seconds) flight. It might be as much as 4 and a third seconds off at the end of the flight.
This, however, is a very artificial scenario. The signal must be precisely on frequency or the satellite will have trouble extracting the modulation. The Inmarsat-M sets I worked on had temperature compensated oscillators, TCOs, good to the 1 ppm sort of level. ACARS is a simpler protocol. It MIGHT only require 5 ppm. I do not have the ACARS specification (or Inmarsat M) at hand anymore. Inmarsat marks them as proprietary so I properly discarded my copies when I left the program.
5 ppm is 20 times better than the scenario above or 0.216 seconds per 12 hour flight. It would be within a second over 10 days.
There is one more consideration, is there any procedure for setting the ACARS time estimate before each flight or is it "automagic?" I would "presume" there is a precision 1 second time tick and other means of sending that tick's actual GPS time value around the aircraft. I'd be pretty sure that ACARS snarfs up that estimate and uses it for continuous internal time updates. So having ACARS a millisecond off timing is not likely. The only real ambiguity is when the time stamp is applied to the signal. It seems to be part of the ACARS message itself. So it must be applied as the message enters or exists the transmission queue. (And, with time a part of each ACARS message it's self-time-correcting to fractions of a second.)
IMAO the time tick should be when it entered the queue. This accident shows that this might have helped unravel some of what happened. (And the NYSE recently discovered that makes a BIG difference when you have computer traders that will game a situation such that the queue becomes longer than 1 trade. There is a credible theory that's what brought the market down in 2008. That shows two things, this is an issue that is often poorly considered in system design and that this may also be the case in the ACARS system used on AF447.)
I hope that swats down ideas that the clock times could be materially off to say 10s of seconds or more.