You certainly can. You won't be able to make use of the schema tools for JSON content, but the Logic App can still receive it. If the files you are trying to transfer are large enough, you may need to enable chunking for the Logic App to accept it.
The Create File action won't show the message body as an option by default, but by choosing "See More" in the dynamic content window you can access the body of the HTTP message.
If you are concerned about data security, be sure to set up secure access in your Logic App design. If you do not configure this the request content is available in places like the run history. You can read about how to do this here: https://learn.microsoft.com/en-us/azure/logic-apps/logic-apps-securing-a-logic-app#obfuscate