Yes, they are. Status currently uses Whisper, the messaging protocol of the Ethereum stack.Whisper provides peer-to-peer messaging with zero reliance on centralized servers, data centers or service providers.
Every message is end-to-end encrypted, and broadcast to every single peer in the network for a set time. This makes it not only impossible for unintended audiences to read the content of messages, but also to see who sends messages to whom. For private 1:1 messages, only the intended recipient of a message is able to decrypt the content. For public chats, anyone who knows the name of the chat can decrypt the content.
An additional safeguard is the use of a new encryption key with every message, after the initial key exchange between users (Perfect Forward Secrecy). If your message key is compromised, only the message for that particular key is compromised. There is no access to past messages.
The privacy Whisper provides does come at the cost of high data usage. Development of an alternative is ongoing. You can follow progress
here.