I'm not entirely sure what you are asking here but,
Alfresco can manage web content which is then deployed to a web site; take a look at the WCM functionality. It can also be a powerful "back-end" for supporting a public facing website. It also has a new and powerful web script front end which you may (or may not - it's your choice) find useful for your public website.
I have been manageing several websites through another hosting company for four or five years, and I have a pretty good understanding of LAMP systems. However, since it is a shared server I don't think I have access to the root. I have used many open source applications (e.g. WordPress) which are very simple to upload via ftp without any special .exe or installer packages. You just create a MySQL database, alter the config file and upload. Then it's ready for use.
What I am confused about is the way in which Alfresco installs. Is there a way I can put the product on http://www.mywebsite.com/alfresco without having access to the ROOT of the web server?
I think the the answer is it depends on what infrastructure your hosting company provides. But probably not.
Alfresco is far more than just a web tier and requires a java application server. The quick installers install a small application server for you (Tomcat) to get you up and running.
If your hosting company has a java application server that supports remote administration such as WebSphere then you would be able to install the Alfresco WAR file remotely without access to the root filesystem.
But even then features like CIFS may require O.S. level configuration because they are not web tier technologies. And a production quality installation would also be concerned with configuring the RAID file-systems and how data is backed up as well as how much machine resources (memory and cpu) to allocate.
A better approach may be to find a provider to host Alfresco for you. Alfresco can be shared by several tennants, so you should be able to get access to a shared Alfresco server.
