Not really, no. But that might be due to my lack of experience with Unity.
My understanding is that the IK functionality in Unity is a unity-specific solution that you add on top of a rig, it's not a property of the rig as such. The IK solution in blender is very blender-specific and is unlikely to have a correspondence in FBX. And Unity import from .blend files is done by first converting everthing to FBX behind the scenes, or at least that was what happened when I looked at it a few years ago.
Best I can come up with is converting the IK animation to FK before exporting, which would need to be done via a script.
Other people seem to have run into the same problem:
https://blender.stackexchange.com/quest ... fbx-format