Once you signed a document, it means that you are declaring all information on the document are correct. That is why we always say that you do not sign anything without checking the details.
In the case of primary school applications, if the address in fact is not your real address, and you declared (ie signed the document) it to be your real address, that is fraud.
You are cheating the other party who receives the signed document. So legally, you can definitely be sued by civil litigation. And since "the other party" is the government, I am not sure whether there are additional laws/rules that qualify it to be a criminal case.