The only reason I'm posting this in here is because it has to do with web more then the actual drive.

Anyway... Is it possible to use an external hard drive as a server just to access information (docs), not host, as long as it is connected to a computer that is connected to the Internet.

The hard drive could be used as the the actual location of the files. If you are talking about the apache web server, then this could be accomplished by placing the htdocs folder on the external hard drive.

The actual server software would have to run on the computer though. Meaning that the hard drive only stores the data. The main processor and RAM would still be utilized.