ScoTTel,
I don't know if this will answer your questions as it's been awhile since I've worked on one (in fact it was when they first came out and even Avaya Tech support couldn't help). However, this is what I learned...
No, you don't need to use Avaya's web hosting service. You could use the device as a web server but (and this may have changed over time) the server was only running FreeBSD R1 and offered limited ability to 'create' a web site. As I recall it didn't support MS FrontPage extensions, only a few CGI scripts, no Python or Perl. Although FreeBSD is a very good Unix like software and is used by many large ISP's, Avaya didn't do it any justice by basing their server on it. As far as connection, like any server you want to connect to the internet, you will need a static IP address from your ISP, a registered domain name, etc.
That being said, if they no longer use the Unix platform, I did a lot of typing for nothing. If they still do, and you are familiar with Unix or are willing to learn, I'd say go for it. You can always upgrade the software because FreeBSD is, well, free (if you want the CD version, I think it's about 5-10 dollars. All in all, it was a blast to play with, in fact, I have a computer at home that I run the BSD software on (as the network server for the home network).
Hope this helps
franke