Shrinkage is caused by three things: water, heat and movement. To answer your question, the spin dry on you machine should not pose a problem except on clothing sensitive to "mechanical shrinkage like cashmere, angora and other luxury wools". Water, no matter the temperature can make fibers shrink. It all depends on the weave, construction and fiber. There is no "one rule" about clothes. Who remembers rayon in the 80's when it shrunk in the rain? Heat actually is not a "cause" of shrinkage but it is the catalyst that makes the shrinkage caused by the water visible and even worse. The heat removes the water and the fibers shrink much like a kitchen sponge shrinks when it is dry.
Anyway, the simple answer is no, in general the spin cycle will not shrink your clothes. The other person is also right in saying that today's machines can do the same as hand washing with the exception of over sized items or "dip and hang" clothes.