I'm playing devil's advocate a bit here. It could be, but the "fourth place" idea is, as yet, more of a concept than a particular kind of physical space, I think, and as a concept it is at least as much a virtual as a physical space anyway. People discussing the idea emphasise its fluidity, even mobility. It's a place that users turn into a fourth place by using it in that way. It seems a little alien to the idea to build a space and call it a "fourth place", in this sense. In relation to libraries it denotes a way of using the library space. Since this is number 4 on the list it could simply be a fourth place whose functions are undefined, as it clearly is here, for example:
"En complémentarité aux trois équipements de proximité (Prévert, Picasso, La Butte), la ville d'Echirolles a récemment inauguré un quatrième lieu dédié à la jeunesse et plus précisément aux 16-25 ans."
http://www.ville-echirolles.fr/citoyennete/quartiers/cpt/ech...