Of course they do, you can file a request so they would send you what info they hold. I did so. They store everything - your every message, all login dates, device metadata and anything else you can think of.
The best part? They say that the messages you send are like email, so they are not obliged to delete them.
Wouldn't it be MIUI without a coat of paint, considering this is their plan B system without or with limited Google services?