I'm not sure the CPDLC gets it's flight number data from the ACARS.
I've flown both the 777 and the A330 with inop ACARS and the CPDLC still worked and had the correct data.
The ACARS is only for company comms/ admin stuff/wx etc
The FM or FMC sends the data to and from the CPDLC ADSB units directly irrespective of ACARS.
( yes I agree it also sends data to the ACARS as well )