Well, I just tried it and it worked! If you needed a quick and easy web server set up, you could grab a micro instance of a virtual machine on Amazon Web Services (AWS) EC2 service, set up Apache or similar, etc.
However, it's much easier than that. S3 (Simple Storage Service) lets you serve files, including static web pages, directly. You create a bucket, upload files, set permissions, set up logging, and you have a web site. It's free unless your web site has a huge amount of content.
Of course this is static, i.e., there's no PHP or programming, or dynamically generated pages here. This is just a simple site, but it works quite well.