No. Over most of the earth the lines of magnetic force are travelling parallel to the surface of the earth, but as you approach the magnitic poles they turn and eventually become vertical. If you are standing at the North magnetic pole holding a compass as you normally do, horizontal, then the needle will try to rotate to point downwards. Some combination of the case or the spindle or both will stop it doing this. If you were to stand the compass on its edge, then the needle would point straight down. This effect is seen to a degree all over the earth, it's called the angle of dip; approx 0 degrees at the equator and 90 degrees at the magnetic poles.