It is quite common for a single click on an item in the tree to both select that item and expand it to show its children. This is used in a context where the item being selected already accomplishes the primary action, eg. in Windows Explorer selecting the folder in the tree will show its contents in the right hand pane.
It is however also usually very unclear wether you should be single or double clicking. While it's usually understood that a hyperlink or a button require only a single click, there really nothing that says "double-click me". In fact many people will double click everything just to be sure. And who could blame them? In OSX applications launch on double click, except in the Launchpad view: there is no consistency anywhere.
I would therefore advice against double click for selecting an item and immediately closing the dialog. A tree, unlike a list, is a complex UI that requires quite some interaction. A user should not have to fear accidentally selecting the wrong item and closing the dialog just because he clicked too fast.
If it's preferable to have a single select+close action available, for instance because a user needs to interact with this UI a lot in his workflow, I would suggest offering a separate control to accomplish that. To not clutter up the interface you could surface this on hover of the item. I don't think this should replace your select->ok flow, but it could be added to it.
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