It should. Give it a try.
The concept of a "page" doesn't work that way for a library (or a snippet), but either one could contain all the objects in a single unit for a page that you insert normally into another document (I do this for filler pages for an directory I make once a year).
You could also save pages as documents and combine them with other documents in a Book (.indb), or open them and use the Move Pages command to add them to another document.
@Peter – There is one detail I want to add for both concepts, library assets and snippet files.
Of course, all the contents of a page or a spread (without the ones comming from an applied master spread) could be stored into as a single library asset or a snippet file. Page information is not stored. Using library assets or snippet files will never add master spreads to an InDesign file.
However, what is stored is the relative position of the contents in relation to the geometrical center of its spread. But this fact is not obvious for the "average" user.
When working with assets and snippets one can retain that relative position.
With library assets:
Place assets of a library with the place command of the library.
Do not drag the asset to the page.
Hold the alt key when the place gun is loaded with the snippet and click.