from my basic testing not it does not access the internet on startup,and I set the firewall to block all access to networks by sins then started it , it started a bit slower,but operated normally,but I do not use zonealarm security suite because I prefer specialist software for each part of the defences, ie zonealarm free for the firewall, avast for the antvirus,spybot search & destroy adaware and spyware blaster for antispyware, and serveral antirootkit tools for antirootkits.
for your problem I think that the suite might need to checkout the program controls and any parts of programs such as dlls etc in the sins directory and allow them to have local access,sorry but I do not know the suite well enough to advise exactly what settings to alter in it
harpo