I think you should try web app disabling the internet on your phone. Have you tried it? If watsup store the messages on its servers, it would be able to retrieve. But this is also not reliable since they may check phone connectivity before they retrieve from their "servers". I am still skeptical that they may store on servers behind the scene at least for speed and performance.

I just opened the Whatsapp web app (never used it before), and then immediately set Airplane Mode on my phone as soon as it scanned the QR code.

WhatsApp managed to load all my conversations (I don't have many) and the most recent message, for display in the list-view. But each conversation only has the most recently sent message. After a while I got a "Phone Not Connected" message. Seems like it really is only stored on your phone.

>they may store on servers behind the scene at least for speed and performance.

Yes, that's why I think so. They easily loads all the messages and images in just few seconds even when my phone's internet is too slow.

They won't let you use the web app when you're phone is disconnected, so there's no way to confirm it.

In order to use Whatsapp Web you need to be on the same wifi network as your phone.

Your phone has the data on it. Intranet speeds on most wifi networks these days is faster than 50Mbps. That's more than fast enough to transfer all your messages and photos with little to no lag.

It doesn't matter how fast your connection to the WWW is because you're not using the WWW to transfer the data, you're using the wifi intranet.

It will work over a mobile connection, using wifi is only recommended to save data usage.