It's unclear from your posting if you're asking about ArcGIS Server or enterprise geodatabase
connection (or both). A graphical representation of the networks and nodes and software suites
would go a long way to explaining the problem (and will likely provide the answer).
Generally speaking, you need full network connectivity in order to create a connection. I connect
to both database and ArcGIS server nodes in my office through VPN all the time, but I could not,
for example, use my Linux box to connect through my Win7 laptop's PuTTY session to remote nodes
without making significant modifications to various firewalls and custom-coding more network
proxies than I'd like to -- Just because you can get to two nodes from a location doesn't mean
they can talk to each other.
- V