I work in. school admissions for a Local Authority.
Please report it, anonymously if you want, but please report it,
Return to Sender can take weeks, sometimes months to get through the system as they are not given priority by the post office.
It is very possible they will be found out regardless, the school may report back to the LA of a change in address. Some schools ask for proof of address, some rely on the LA checks.
It will be so much better for all involved if this is nipped in the bud now. There is the chance to get on the waiting lists now while there is still movement - not after school has started and the process has settled down.
Places are taken away from children, even after they have already started!
With regard to address checking in general - there are many different processes across the country.
We manually address check all applications, unless the first preference school is oversubscribed, or it is clear that they will be allocated under a higher criterion (medical, Looked after, etc).
We also re-check some of our most over subscribed schools after the offers have been made (the nice little middle class schools that people cheat to get in to) - the number of parents who split up in the winter and child moves into a smaller flat near the school, only to reconcile a few moths later and move back to the old family address is surprisingly high.
People use family addresses and change bank details to that address, even register with doctors from addresses they don't live at. We've had falsified documents, sob stories, lies etc
They do get found out, if we don't catch them other parents will tell us, or schools pick it up on home visits or talking to the child.
You will be making life easier for everyone to tell your local authority now.