Broadcasting the transaction using a VPN may enhance your privacy, but you should know that privacy is not only related to broadcasting the transaction, as you can be tracked if you search for your address in some block explorers. Some Electrum nodes may even record your IP/Bitcoin addresses list, so managing a full node Using Tor with an open source block explorer, or at least connecting Electrum to Tor, will enhance your privacy to a reasonable degree.
You mean blockchain.com wallet, right? That's not a safe way to store or manage your cryptocurrency because blockchain.com is not an open-source and is controlled by them, i.e. by 3rd party. Never make yourself dependent on 3rd party when you decide to store or manage your cryptocurrency.
Sometimes you may set up whitelist IP addresses to access your account on Blockchain.com, and if you do that, there is no way to access your account except through your wallet seed. So using a VPN here may cause some problems.