Just like in grip racing (NASCAR or IRL is the perfect example), a banked turn will help to support a portion of the lateral outwards force that is experienced when a car changes direction. This force acts in a direction perpendicular to the tangent of the car's tracjectory (or, in the direction of the gradient of the curve at the car's point along its path if you want a more appropriate terminology).
It takes a little static physics and trigonometry to figure out what the magnitude of this force is at any isolated point in time, and will ultimately depend on the car's mass, velocity, and on the angle of the bank. The supporting force exerted on the car by the bank will act in a direction normal to the track surface (whatever angle that ends up being).
The way I have represented the problem, once the parameters I have specified above are defined by constant numerical values the supporting force may be determined - it should be independent of how sharply the car is turning, or if it is gripping or drifting, just so long as all 4 wheels are on the bank. There will be an upper limit to how much force the track can contribute, is what I'm saying (NASCAR driver's dont understand this, that's why they smack the walls so much

)
You can find the supporting force for the entire duration of the banked turn to see how much the bank actually helps you corner over a larger time scale, but this would require the use of line integrals.
ok, think I've nerded this place up enough for now...
In short - yes, you're right and your friend is wrong.