Yes of course! This isn't as crazy as it seems.
A chat with yourself is a great place to store information only you can access. It is useful for taking notes and making shopping or todo lists or even for starting that first novel.
1) From the green plus icon, Click Create chat to start a new chat
2) Name your chat as normal, but don't add anyone to it, then hit Start. A chat will be created that only you can access.
3). Use it for sharing notes with yourself, between desktop and mobile, storing files, photos.. whatever you need.
You may rename it at any time or set an icon just like any other Chat. Should you decide to open your thoughts up to a wider audience in the future, you can even add other people to it at a later date.