If it's "your desk" where "no one else sits" then it would seem unlikely that you're in a co-working space. If you're in a place you call "the office" and other people have easy enough access to "your desk" to unplug your laptop, it probably has an open-plan.
If none of this is true, you might as well be talking about purple dogs stealing the umbrellas from your hamburger patch.
Most co-working spaces that I've looked into had options for fixed desks. Even if they don't, it might be nice to think you can go get lunch or a coffee without someone taking your desk (or ethernet cable)
If none of this is true, you might as well be talking about purple dogs stealing the umbrellas from your hamburger patch.