How does compose handle components that are out of view (ie. off the left or right of a view). Does it just ignore them until they are on visible?

There is no special default handling of off-screen views right now. Views will get laid out, Canvas commands will still get run, but skia is probably smart enough to ignore the operations that are given to it (not entirely sure). Some specific layouts like AdapterList/LazyColumnItems will avoid composing/laying out/drawing/etc views that are off screen but that logic is done at that layer

Drawing commands that are offscreen get culled away yes