No, that’s what a second place is. A third place is for socialization, a second place is for work. Just because you’re relying on some independent small business owner to pay rent for your desk while you prevent other customers from patronizing the establishment and don’t talk to anyone, doesn’t make it a third place.
Agreed, but with a caveat: It goes back into "third place" territory if they're engrossed in a laptop-hobby rather than laptop-employment, even though many of the external favors are identical.