Suppose one has an active lease and pays rent for an accommodation but often travels and stays in hostels or with friends, and they are arrested and asked for an address. If one declares that one has no fixed abode as one is seldom there and cannot conveniently receive correspondence there, or simply that one moves around and stays with various friends is that illegal?
You could be charged with a criminal offence if you give the police false information.
If it is true that you rent a particular dwelling but you are often not there because you travel a lot then it is not illegal to say so to the police.
The common understanding of "no fixed abode" is homelessness.