The previous LA will act on it once they disappear, because the school has to notify them of EHE as well. If you actually read the CME (Children Missing From Education) policies for LAs (I don't expect anybody who doesn't literally do this sort of tit for a living to, but it completely contradicts the perception of EHE and moving = freedom from pesky child protection procedures), they all require schools to notify them of this before they have permission to remove them from their registers. As soon as this happens, the original CME team then get checking for the change of address and when it's found - which it will be, you don't get benefits including housing costs without evidencing a new address - they notify the new area which is, being Scotland, very, very thorough about these things. And that's before you add in the information provided with the risk assessments and potential SS involvement when this all gets put together.
Oh, and they'll contact RD as well. Best not to piss him off too much when you're already taking his children away from him, eh?