Gmail lets you choose another account to use as the "sent from" address and to which replies will be sent. That way the send-only account's inbox will stay empty. To prevent replies and other mail sent to your special iPhone/iPad send-only address from being displayed in the device's unsecured mail program, set the new account to delete incoming messages after forwarding them to your regular mail account. Some recipients are bound to add your send-only address to their contacts list (or more likely have it added to their contacts automatically). Since you'll use the new address only for the messages you send from the iPhone or iPad, the only mail you'll receive at the account are replies - at least in theory.
To read your mail, you use either Google's Gmail app for iOS or your browser to sign into a password-protected Webmail account.Disable all other mail accounts on the iPhone or iPad.Forward mail received at the new account to your regular inbox to ensure you don't miss replies to the messages you send from the iPad.