Karl,
This is totally doable but just remember that if you are not using a VPN to secure your network connection anyone who can "see" the traffic will be able to intercept the audio of your call. Even if your use SRTP it turns out its not that secure and "easily" decrypted. Also you will have to open up a lot of ports from the internet into your CIC phone system which could open you up for hacking or DoS attacks. Depending on how you secure your server you could have hackers registering SIP endpoints to your CIC server and able to make calls out of your phone system. There are special routers you can buy which support STUN which can mitigate some of the port opening issues but its still your best option to use a VPN.
Thanks,
Mark