A https socket is a plain socket connection, the problem is that the protocol is much more difficult since you'd have to implement the entire SSL yourself, on top of the actual HTTP protocol. So, is it possible? Theoretically yes. Has anyone actually succeeded in scripting it completely? I really doubt it, I'd be interested in seeing it done though.
My suggestion is using
stunnel. You configure stunnel to forward a specific port on your computer to where you want to connect using SSL, and then in mIRC you connect to that port on localhost to have it forwarded to the host and encrypted. Then you should be able to speak unencrypted HTTP to the other side afaik.
