It will depend on the detail.
But in practice, yes, I'm absolutely sure they will breach GDPR.
The track-record says they will.
They model themselves on DOGE, which has shown contempt for the law of every kind.
The big-data industry in general is built on a contempt for GDPR, and a model of "It's easier to ask for forgiveness than permission" and indeed, "Asking forgiveness? Hahaha, wotcha gonna do about it, sucker?"
Brexit campaigning was partially conducted via a massive misuse of personal data at the insurance company owned by Arron Banks, now a Reform politician. IIRC he actually turned one of his insurance call-centres into an cold-calling push-polling centre using personal data which had been acquired for the purpose of offering insurance (ie an illegal change of use). IIRC it caused some distress among his insurance staff who were being ordered to make the cold calls – very much not the job they'd signed up for.
https://en.wikipedia.org/wiki/Arron_Banks
Further, when I hear "software engineers working for free", I wonder whether the engineers are working unpaid, or whether they are being paid by some actor which is not Kent County Council.
I would absolutely expect it to be the latter. So then you have to ask Who, and Why.