It is possible using sockets, but that would require a very decent knowledge about mIRC scripting, the HTTP protocol (especially the POST method) and sockets and HTML in general. Sockets only provide the most basic connection, you have to script the protocol to the server yourself.
There are some sockets tutorials out there (google, or search this forum, expand date range to a few years), but you'll still need to find out exactly what to send to the web server, and how to process it's response.
If you can paste the entire HTTP connection with all headers, and tell how that data is stored in mIRC, I might be willing to get you underway.