More like using Tor to create a FB account with made up information and expecting FB not know who you are because your IP is obscured and you use fresh browser profile. In your DNA doesn't tell your identity, there's DNA everywhere and it's not something hard to come by. The analysis is only valuable if can be connected to a persona, otherwise its just chemical reaction.
No, your analogy makes no sense. A fake facebook account is not identifying information. DNA is. They can figure out who you are based on the DNA alone, if they have enough data from your relatives.
There are billions of addresses in the world and you can look it up online. It is an identifying information only when it is attached to an identity. That's exactly the same. DNA is everywhere, it's only identifying when connected to an identity.
They can match me with my DNA if they already have complete knowledge of my family structure and all their DNA. So if all Kardashians but one send their DNA for tests providing their true identities and the last one sends anonymously, they can assume the identity of the last one.
So yes, there's a risk but its not much different from going outside and leave behind hair or saliva unaccounted for. That's Putin level of paranoia IMHO(he is known to have men collecting his poo etc. when outside).
Maybe can be useful for insurance companies to match you and price you according to your DNA but they are not allowed to do that and they can only exist within legal structure.