Some forks are described as "integrated", and others are described as working with both integrated and external headsets.
Is there any reason why an "integrated" 1 1/8" fork wouldn't work with a conventional external 1 1/8" headset?
Some forks have an integral moulded race that's designed to fit an integrated headset. generally those forks won't work with an external headset, or if they do you'll get a gap between the fork and the head tube. most integrated headsets do come with a crown race though, so you can use a non-integrated fork.