I have only played with the shatter effect for a matter of minutes.
I want to have a bottle fall and hit the floor (the lower half of the screen) and shatter, with the glass shards sitting in place on the floor.
Right now, AE is making the bottle shatter and all of the shards disappear offscreen. Will AE allow me to shatter the bottle and have the glass remain in place for the duration of the cmop?
Not really. Shatter does not have any built-in collision detection or any of that. You can face it to some degree using custom gradient maps and animating the forces, but then of course you can't use the built-in patterns and will have to draw all the segments. Another alternative might be using time-remapping on the pre-comp, but since the forces are still radial, you will never get the fragments to rest perfectly anywhere. Rather use multiple instances of the effect here and compliment it with others, then mask out the parts you don't need and add some form of "invisible" transition here and there with animated and feathered masks and cross dissolves. If you e.g. add some heavy DOF blur that would further disguise some of the stuff....
You'll have more luck mixing shatter and a particle effect like Trapcode Particular than trying to do the entire effect with Shatter. If it were me I'd do the breaking bottle in a 3D app using camera mapping to align the geometry. Blender is an open source option that works well with AE in it's latest builds.