Electrum is a SPV wallet and you have to connect to Electrum server to broadcast your transaction.
Even if you set up your own node it will still connect to Electrum server?
To be detailed, Electrum can't connect directly to Bitcoin node. You need to also run Electrum server (which obtain it's data from your node) and configure Electrum (the wallet) to only connect to your Electrum server.
I think OP's concern is related to anonymity rather than privacy.
The distinction?
In short,
1. Privacy is about hiding your action
2. Anonymity is about hiding your identity.