Apache support for weird SNI request

Server
15

You mean a complete HTTP request? Sure.

POST /some-custom-path HTTP/1.1
Host: my-weird-domain.com
User-Agent: SDK/1.0
Host: my-weird-domain.com
HTTP_X_DATA: some-custom-data
Content-Type: application/x-www-form-urlencoded
Content-Length: 305

and the content is URL-encoded form data, like such:
parameter1=value1&parameter2=value2&parameter3=value3

Or were you talking about a different log?