It can, I have never had a problem with avast program updates on my XP Pro system, nor my Windows 7 netbook.
Then again we know nothing about your system setup and I'm not using ZA, I gave up on that many, many years ago before I came to avast, over seven and a half years ago.
I installed Agnitum Outpost firewall, the free version 1.0 and have been with it ever since, upgrading to a lifetime license from Outpost firewall Pro 3.0 through to the current version of Outpost Firewall Pro 7.5.1.