Yes and No.
Yes - To connect to a DB, you can either have a DSN or DSN-less connection. DSN requires you to set it up on the server ahead of time. DSN-less creates the connection to the DB on the fly from the ASP code.
No - You cannot have ASP without IIS (well, there are some offshoots of IIS.. chilisoft, or something, has an ASP-like language, but I'm not familiar with it). Without it you're not gonna get anything. IIS receives the request for a page, checks to see if it's there, checks its security, executes the code for it, then serves the results back to the client. But IIS is not required for a dynamic website. There are other web servers such as Apachi, WebLogic, WebSphere, and many more, but ASP is pretty much unique to IIS.
That which does not kill me postpones the inevitable.