The SafeZone is completely isolated from your regular desktop. It is a virtual environment which can be cleared and start from scratch again. If you encounter a piece of malware whilst in the safezone avast would alert in the normal way.
But your question isn't about what the safezone is for, its use is essentially for things like internet banking, where it uses the safezone browser, which is built into the safezone, so you aren't having to access your regular browser which is outside of the safezone.
So unless you were using webmail where you view your email through the browser (the safezone one), then you wouldn't be using your email program in the safezone.