max_godot
As far as I know Godot will only import rig bones, its keyframed animation and shape blend from Blender. Things like constraints, modifiers, and anything procedural created there are ignored. Before exporting, make sure to apply any modifiers and scale to your model, check normals facing correctly, and bake any procedural textures and procedural animations that you have. Keep your model/rig as simple as possible when export.
You then do your bone constraint using Godot. But last I heard Godot IK is not very good and is being reworked so you have to do it manually using your coding skills.