Yes, the photos are indeed stored on the server for some amount of time. If you dig into the obfuscated messages.db file from WhatsApp (I don't know about now, but it used to be encrypted with a known key, and there are tools for decryption available), you'll see that it stores a tiny JPEG thumbnail and an HTTPS URL on their servers where the photo can be retrieved. Though if you try to get to older pics you are just presented an error message that it's no longer available.