Most certainly, but this is not where the challenge is, the challenge lies within the difficulty of actually cloning the tag on those goods.
those tags use what's known as a UI or "unique identifier", the UI is a part of the chip physical existence and not just some sort of binary stored on it,so you can't just clone it, you need to be able to manufacture one that has the same exact private key, so nothing but brute-force will help you, and if you want to go that router, try Satoshi's wallet it has more value in it that a shoe tag , so now think of this as a private key which is not stored on the blockchain.
The NFC chip also has a public key stored in another part of the chip, known to everyone and can be read using any RFID reader (your smart phone for an example).
Now once they make that pair of shoes and assign the NFC tag to it, they add that piece of information to the blockchain (just like when a miner finds a block), now everyone knows the public key to that pair of shoe but only someone with access to the private key which is stored in that tag can sign a message on the blokchain to prove their ownership, you use the app that Nike or whoever product is as a block-chain wallet, the app (reader) can request the tag to sign a message using the public key and the private key, without knowing the private key your app knows if the signature is valid then the private key is correct thus the tag is real and pair of shoes is actually authentic.
if the encryption algorithm is compromised, knowing the public key will allow you to know that private key ( not a very serious threat "long story"), also by knowing a single private key, anyone will be able to make a dozen of the same tag and they will all "look" authentic on the blockchain, unless the manfuaturer has the ability to simply delete that piece of information from the blockchain which then is not a real blockchain to begin with.
But overall, this is pretty secure IMO, if they want this to be super secured, they could put this on a POW based coin and have people secure it for them.