The trunions are movable under the saws table. This allows for alignment of the blade to miter slots. If the blade is not square to the track it wont make a difference to the squareness of the piece cut. It will as you suggest make a ratty edge. This is called 'heeling' when the back of the blade is cutting outside the kerf. There are lots of article and probably books on how to tune up a saw. To take the affect of heeling even further to a useful purpose. It's possible to cut very large coves on a table saw by setting a fence at an angle and pushing across the blade in a sideways fashion. light passes, great care and danger is involved. read up on this before trying it at home.
Bill