It is possible that your security suite reports some system access on your PC. This will be with the sole purpose to make use of your system as a hosting environment (e.g. launch a process, open a file, ...).
An example dialog that you might get is the following (ZoneAlarm in this case):
The reason for this is, that we launch a process to read in some special files that are used for the themes of the graphs (used in the displays). This is no security risk, and you should allow it, or ICE will not be able to open (it will report an error and exit).
Outgoing/Incoming Network Connection
It is possible that your security suite reports an outgoing or incoming connection when you start ICE.
One of the possibilities is an outgoing connection to the internet, that will check the digital signature of one of our 3rd party assemblies that ships with ICE. The sole purpose for this is to check whether your dlls are not compromised, in order to prevent you from hackers. It is safe to allow this access, since it will just verify a certificate with one of the registered certificate servers on the internet (e.g. VeriSign). You may however also block this access, and ICE will still be able to launch successfully.
Another possibility is an outgoing connection to other software environments on your system. If you have configured an open software infrastructure, where ICE can make use of other software environments, it is possible that this travels over TCP/IP, or any other communication channel you've configured. Your security suite might report this, and you have to allow it in order to make use of that functionality. However, normally this will only use your internal network (LAN) and not the internet (WAN), unless you explicitly configured it to do this.
Finally it is also possible that you want to use it the other way around, where other software environments can make use of ICE. In this case your security suite might report you that ICE is functioning as a server for incoming TCP/IP connections, or another communication channel that you've configured. You have to allow it if you want to make use of this functionality. However, normally you will only allow it to server on the internal network (LAN) and not to the internet (WAN), unless you explicitly want to use it over the internet.

The ICE software will not make any outgoing connections, with specific functionality to break your privacy. ICE will never communicate with any of our servers. Nor will it communicate with any other server for our purpose. We also check the integrated 3rd party assemblies that we use, to make sure they comply to this rule.