Yes it does. It has network shield and anti-spy/malware function.
with that being said does it make sense to turn the anti-phishing feature off on ZA then?
Don't know, never used ZA. Patience, ZA users are around this forum, just not all day. One will likely post and tell you the correct course of action.
Edit your original post to change thread title to something like
"ZA-Avast! Free compatibility question" to get response quicker maybe.