Make a site publicly accessible?

Currently we have a Geocortex implementation running behind our Firewall. That implementation has a number of internal sites. We have now built another site that we would like to make accesible to the public to use, and we're not sure how to make that happen. We have an "external" server that we host our externally accesed applications, with an ArcGIS web adapter on it serving our ArcServer REST endpoints. But it is not a reverse proxy or in a DMZ. Our network guys have said they could just route traffic through there and "point" it to the link of the site we want to make it publically avalible, however I'm wondering if that will impact the use of the various workflows, reports, and Instant Search abilities. I've reviewed the docs, but they've been little help. Does anyone have an expireance or advice in this matter, that could help point us in the right direction?