Can I use same MTB fork after changing headsets?

hi, I'm about to change my frame from a hardtail schwinn to a FS Giant VT-2. I'm hoping to just swap the frames with out buying new parts. My question is, can I use the same old fork even if i change headsets? I'm changing from a FSA Threadless headset to a Zero-Stack headset (Zero-Stack is like and integrated headset which the bearings fit inside the frame). Frame to frame measurements are the same, but the Giant VT-2 uses a different type of headset compared to my old schwinn frame.