HTTP/1.1: Status Code Definitions
How well a 413+close works depends on your web framework's support for close-after-response and the way your client reacts to a closed connection. It may be that the client will not read the response until the request has finished, in which case closing the connection mid-request will prevent your client seeing the 413 response. It might not be too bad if you were to use scripts to upload files, but on a form submit I think closing the connection would be catastrophic.