This feature isn't currently available in Kiln and it's unlikely that it will show up on our roadmap. While the feature would certainly be useful for some people, we have to be very cautious of feature-creep in Kiln. Adding FTP functions falls under that umbrella at this stage.
That being said, I'm not here to read the minds of the community, so if anyone thinks this feature would be helpful, please upvote the question (not this answer!) and let us know! We've re-evaluated our positions in the past and there's no reason it can't happen again.
As another option, Mercurial itself does transfer data from place to place pretty well. So a better method might be to install Mercurial on the web server and have it pull changes from Kiln whenever there's a push to the stable repository (you could even alert it to new changes by setting up a webhook and some server-side coding) then just serve the local (to the web server) repository as the site. That would eliminate two data transfers from your process and allow you to essentially keep your website constantly up to date.