Comment 4 for bug 526453

So, the rationale here is that hiding the searchbar means that you're getting rid of the multiple search functionality, so the default engine is probably the best bet (as opposed to whatever you had last before you got rid of the searchbar).

Options are:
1) Reimplement the dialog
2) Remove the menuitem/disable the keyboard shortcut when the searchbar is hidden
3) Expose a means to make an engine the default in the search manager.

I'd go with 3, myself, but I'm not married to any particular solution.