Yes, scripts can access properties of other windows in the same domain that they have a handle on (typically gained through window.open/opener and window.frames/parent). It is usually more manageable to call functions defined on the other window rather than fiddle with variables directly.
However, windows can die or move on, and browsers deal with it differently when they do. Check that a window (a) is still open (!window.closed) and (b) has the function you expect available, before you try to call it.
Simple values like strings are fine, but generally it isn't a good idea to pass complex objects such as functions, DOM elements and closures between windows. If a child window stores an object from its opener, then the opener closes, that object can become 'dead' (in some browsers such as IE), or cause a memory leak. Weird errors can ensue.