Would my performance increase if I manage visibility of these randomly placed items so that only the ones within the stage display?
It might help. Starling won't render display objects that are set invisible. However, you also need to loop through them every frame to manage the visibility, so that will take away some of the extra gained performance. I can't say how much. It depends on the content. You should test this out yourself.
Would there be a better component that could be used instead, where I can have randomly placed items but virtualized?
The List component would be the only component that could use a virtualized layout with your content. However, using it with this type of content wouldn't be particularly easy. You'd need to create a custom item renderer, and you'd need a way to abstract your objects as data that can be passed to the item renderer. Additionally, you'd need to create a custom layout that could determine which items were in view at any given moment. Ideally, this layout would also try its best to keep the number of item renderers constant so that frequently creating and destroying item renderers wouldn't result in extra garbage collection that would hurt performance. It would be a lot of work, and I can't say if you'd get the reward you were looking for.
Ultimately, while it may be hypothetically possible, but I probably wouldn't try to virtualize a layout with randomly placed objects. Virtualization works better with layouts that are more predictable.