No, the xpub is not published anywhere. Only individual public keys are published and those are permanently stored in the blockchain. There is also no way for someone to figure out the xpub and any related keys given just those public keys.
After some digging, I find out more about the answer.
In bitcoin core, it is possible to NOT broadcast your own transactions with "walletbroadcast=0" option
See more details at https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-July/009422.html, https://en.bitcoin.it/wiki/Privacy ("Tor and tor broadcasting"), and https://github....
The node side of Bitcoin Core treats wallet transactions as any other transaction. They aren't treated any differently from transactions received over the network. So once the transaction is added to the node's mempool, it will be broadcast to connected nodes in the same way that any other transaction would be relayed.
All you can do is to ...