It wasn't clear to me from the example whether you can select any node in the tree, even if the node can't be expanded.
Yes, you should be able to select any node that is displayed. Just tap it. The default yellow highlight shows the selection state. (developers or people with hardware keyboard can navigate using w,d,s,a, keys to change the selection state as well)
It is possible to select a child node, collapse it, expand it again and it is still selected. Hope this helps. :-)