With a watch only wallet, you only can watch its balance and transaction history but you don't have access to its private keys so you can not broadcast any transactions from that Watch-only wallet.
You do not need the private keys to broadcast a transaction, you need them to sign it, what you need to broadcast transactions is internet connection which the watch-only wallet has.
They both complement each other;
• You create transactions with the watch only wallet,
• Take the raw tx file to the cold wallet and sign it,
• Return it to the watch-only wallet to broadcast the transaction.
With this the private keys never go online.