CONTENTdm stores digital files. So theoretically it can store .html, .css, any website archive format, or zip files. However, if individual html and other web files are stored, there are no built-in ways to indicate the relationship of those files. Or a single file for the website is generated, then we do have a size limit of 2GB.
Libraries and archives who have this need usually rely on an approach more like what Internet Archive uses. They have tools for grabbing entire websites and bundling them into a single "playable" file. Internet Archive also provides hosting services for those archived websites (https://archive-it.org/).