When you establish an Internet connection from your phone you end up
with a point-to-point connection between the phone and (one of) the
router(s) the Access Point Name names (what's that called, a GGSN?).
Your reachability is entirely dependent on what that router allows
you to reach.

It is quite possible that the router is configured to forward all net 10
packets that are destined to a global Internet address through NAT, and
to forward all packets coming from NAT to a net 10 address, but not to
forward packets directly from one net 10 address to another.  This would
be an explicit choice by the operator not to allow phones to talk directly
to each other.

Dennis Ferguson

I don't think so, because the 10.0.0.0/8 network isn't routeable on
the Internet.  For that to work, the network gateways would have to
route local addresses between themselves, keeping the traffic on the
isolated network and, while possible, I can't see the operators doing
it.

Mike.

It quite possibly does mean that as far as direct phone-to-phone
communication is concerned.  You'd have to experiment or ask the
network operator (if you can find someone to talk to at the network
operator who even understands the question!).

If I was doing this for a commercial application, I'd probably set up
a central server on the Internet to which the phones connect and
establish a communication channel using TCP. The phones would probably
have to poll the server regularly to keep the NAT active and prevent
the network from closing the connection.  Messages between phones
could then be passed via the central server.  This would be simple to
implement although would require a dedicated server and may not scale
well.

Mike.