Three ways to reduce message alerts
Whether you are on a tight mobile data allowance, running low on battery or just want to switch off notifications for a while, there's always a concern for leaving WhatsApp running on the background of your device. This is specially worrying when you are travelling abroad and want to control those data roaming charges or when you have people messaging constantly at inconvenient moments.
To understand how this works we need to check some settings and assess how often the app is being launched. Despite the notion the app is "always on" what is really happening is that it checks incoming requests from an specific port (you can check it in the Settings) and access the messages waiting for you on the server. So it's basically "always on" depending on how frequently you use it and what apps you use in between.
If you want to get technical, this StackOverflow thread brings some light to the issue. The discussion shows how the app will typically run up to ten minutes after it has been launched but will disconnect if it has been left unused for a while. Something very easy to spot on slow cellular connections is the slight lag launching the app after a while and waiting for contacts and chat views to get refreshed, getting an "updating" label. The poster suggests this shows how the messages are downloaded upon launch and not in the background — a very usual misconception due to WhatsApp being used on different mobile platforms with their own backgrounding restrictions and way to track mobile data usage.
Kill the notifications
There are three ways I can think of to restrict WhatsApp notifications on your device; each of them has its own advantages. Notifications for all apps installed can be managed on the iPhone Settings → Notification Center → WhatsApp. These are the same settings you allow when you first installed the app, now giving you more options to customise the experience. If you are running the latest iOS 7 version, note these are the system notifications, not the banners you get within the app with their own graphic style. Unlike the Messages app, there's no option to disable only the text preview, so you will want to disable the whole thing from Notification Center.
What's important to know for this section is that you can choose the type of notification alert, app sounds, badge icon and how you what those to be displayed on the lock screen and Notification Center if you are not using your phone when the message arrives. This is the place to disable all notifications if you have privacy concerns and don't want anyone to see who texts you when you leave your phone unattended.
The second options is directly on the app's settings, launching WhatsApp, tapping on the icon on the lower right corner Settings → Notifications. Here you can change the new message sound (as long as sound was enabled on the main iPhone Settings on the previous step) as well as the behaviour for the in-app banners. These are the ones you see when you are chatting with a friend and you receive a message from someone else. For these you can set sound, vibration and preview of text within the notification banner.
The last option, which is more suited for switching off notifications at night, is setting up the Do Not Disturb mode on your iPhone. This is a system wide preference that will keep your phone silent at night or important situations where you are normally asked to switch your phone off. You can either select it manually of have it scheduled every day when you go to sleep.
Top image by Felicia Åkerman