Yes you can! If the imported model has exactly the same skeleton structure and joint rotation as the BVH it should work just fine.
In BVH all joints are always Quaternion.identity in the resting pose, in other words, not rotated. If the model imported by Unity has a skeleton with rotated joints the animation will appear incorrect since BVH base all rotations in the AnimationClip from Quaternion.identity. I tried to make a method that adapted a BVH to an already existing skeleton but it was tricky to make it work without some rotations being flipped the wrong way so I couldn't include it in the final version of the product.
I'm currently working on a different product that skins a mesh from a skeleton during runtime, it'll ensure that the joints have the correct rotation. I'm making good progress but I don't know when it's finished. I recommend that you download the demo of BvhImporterExporter and see if you can achieve what you need. The most important thing is that the model's mesh was skinned to the skeleton when the joints wasn't rotated, then the AnimationClip created from BVH will move the skeleton correctly!
Check your model in Unity (make sure it's in its rest pose - you can uncheck "import animation" for the model in the inspector). If all the GameObjects that make up the skeleton have Transform rotation [0,0,0] you're good to go! Assuming that the skeleton has the same structure as the BVH of course (matching bone names).