We would do well to sort out a couple of definitions here. The geographic north pole is the northernmost part of the planet. It is where the Earth's rotational axis intersects the planet's surface. It is actually not a constant location but it wobbles or drifts slightly over time. The magnetic north pole is the point in the northern hemisphere where the Earth's magnetic field emanates from the planet into the atmosphere. It is located near the geographical north pole but they are not the exact same location. Like the geographical north pole, the magnetic north pole also shifts over time to an even larger degree. The angle between the two polar lines is called magnetic declination.
To make matters even more confusing, the magnetic north pole in the northern hemisphere is actually the south pole in the Earth's magnetic field. It is called magnetic north since it it located near the north pole to prevent confusion. Since, magnetically speaking, opposite poles attract one another, the north point on a compass needle is attracted to the Earth's south magnetic pole in the northern hemisphere, so the compass needle always points north.
So, technically speaking, the answer to your question is no. The compass needle points north because the Earth's actual magnetic south pole is located near the geographic north pole. We call it magnetic north to maintain some level of geographical consistency.