I haven't tried this personally, but I think you have a couple options:

1) I think that you can still associate a work item category to a team area, which would be the default team area when a category is chosen, but I think you can change the team area to another one .. .I don't believe that a team not associated to a work item category can't work on it.
2) Or you can created your team areas and your work item categories but not associate them ... I think the association only give the "default" team area for that work item category.  So I think if you don't associate anything, the work item category can be set and the team just doesn't get set automatically.

Susan

Work item categories have exactly one purpose, which is to automatically associated a work item to the team that should work on that work item, based on information that is provided by the work item creator.   So if there is a single team that works on a given product/function, then using product/function as the leaf categories is appropriate.  But if multiple teams work on a given product/function, then it is not.   For each team, you need to find one or more terms that characterize the work being done by that team (and no other team), where that term is one that would be understood by the work item creators.   Then those terms are then your categories.