I'd use this: http://mathworld.wolfram.com/Point-PlaneDistance.html   (Equation 10, signed distance) on the bounding box of the objects.

If any bounding box has mixed positive and negative distances for its corners, it's intersected by the plane

I'd use this: http://mathworld.wolfram.com/Point-PlaneDistance.html   on the bounding box of the objects.

 

If any bounding box has mixed positive and negative distances for its corners, it's intersected by the plane