The fact that it is a web console means that as long as it has been given a public address) or is natted to a public address in the event that it is behind a firewall) means that it will be accessible via the web as any web service will be - regardless of client location.
If you can establish a client-less VPN connection to your network, that would be the best way to access your Orion web site from any computer on the Internet. I suppose you could purchase the Orion additional web server and place it in a DMZ, get a SSL cert on it and hit it as a secure web site. I've never looked up to see what ports you'd need open between the additional web server and your main Orion poller, but I'm sure you could find it somewhere or support could tell you.
Personally, I'd be a bit reluctant to make my Orion site Internet facing. If someone were to happen to compromise the Windows server you're running your Orion site on, they would get a really, really good idea of what your infrastructure looks like!
VPN would be a good option, maybe using something like a Cisco ASA 5505 to keep the costs down ($350). With that you could do IPSEC/SSL or even a Web Portal that puts you directly on the web front end.
Or you could use something like Logmein which installs a client for access...