You can create an ON/OFF pose with the BVH constraint setup. Then when you create a new action, turn ON the pose, "show more than drivers" and open the bones folder of your model (under the action). You will now see a new folder for action objects, which contains the BVH rig, there you can capture the sequence.
You can also just create and save an action with the setup (do not capture sequence). Then when you want to capture the sequence, open the action with your model, capture the sequence, then "SAVE AS" new action. Don't override the original setup action.