I need a simple system to switch one CFL fixture in the middle of a large room with 3 wireless switches around the room with no dimmer.
I presume a Linear PS15Z-2 Remote On/Off Appliance Module would control the fixture.
Will 3 GE 12723 switches control it with no connecting wires?
No apps, no controllers, no timers, just a simple dumb setup to avoid hard wiring because the room is quite large and it would take a lot of wire.
Willy
The GE add on switches work by being physically wired to a GE master switch. They have no network capability themselves. So they can’t work as you described.
However, there are auxiliary switches from other brands which are themselves Z wave devices and which can communicate with the SmartThings hub on their own. This can then create a virtual three-way so that the switch talks to the hub and The hub talks to the device that does actually control the load to the fixture. So good idea, you just need a different model device.
As it happens, the Linear auxiliaries are zwave devices and could be used for this. 
https://www.amazon.com/Linear-Z-Wave-3-Way-Accessory-Switch/dp/B00EAY3K5Y
In order to give the switches control of the fixture even if your SmartThings account is unavailable, you would need to do direct Association, which means you would also need a minimote to set up that association. The minimote can then also act as a handheld remote if you like. But it does mean buying one additional device. ( shop around for the minimote, you should be able to find one for about $20. )
http://www.zwaveproducts.com/shop/brands/aeotec/z-wave-minimote
If you don’t use direct Association, then if your SmartThings account is not available you won’t have any control of the fixture. So another alternative would be to get one master switch in the room that did control the load to the fixture so at least you would have that for control during hub outages.
( this all assumes that you do have a SmartThings hub to handle the message traffic. )
I just noticed that the particular linear pocket socket that you mention does not have association capabilities. This is an optional feature and manufacturers make a decision model by model as to whether they will include it.
There are several models that offer this. There is an older Cooper that works fine and has a number of advanced features, including association.
http://www.westsidewholesale.com/cooper-rfapm.html
Or several of the newest generation Z wave plus modules also support Association, you just need to check each one to be sure.
I think the Zooz line may, @TheSmartestHouse should know.
Again, you would only need association if you want the switches to continue to be able to control the fixture even if your smartthings cloud account is unavailable.
Yes, all Zooz switches support association but they are not virtual add-ons, instead, they can be used as the one master switch to connect to the light. For virtual add-ons to be associated with your master switch, we recommend the Evolve LTM-5 which only requires power (line) and neutral: http://www.thesmartesthouse.com/products/wall-mount-accessory-switch-ltm-5
If you want to avoid wiring altogether and have a battery-powered device mounted on the wall to serve as additional Z-Wave switch, you would probably have to wait for Aeotec’s wall-mote device to come out but it does not look like a light switch: http://aeotec.com/z-wave-wireless-switch
As of today, there is no official release date for the device.
If you want a battery-operated switch, there are a number of options. See the following thread. In particular, the Cooper 9500 looks exactly like their regular wall switch. 
Sorry I wasn’t clear, the OP is looking for a pocket socket module to plug the light into, and then three wall switches to act as virtual remotes.
So I was asking about the zooz pocket sockets, not the wall switches. In this set up, the pocket socket would need to support association so the switches could turn it on and off even if the SmartThings account were not available.
Thank you for clarifying @JDRoberts! The Mini Plug supports 3 association groups, see here: http://products.z-wavealliance.org/products/1911/assoc?noFilename=True
It’s a new product so we have not yet uploaded the full manual online but this plug has a number of advanced features. There should be a couple of custom device handlers for the product available shortly. For now it works great as an on/off switch with power meter. Custom device handlers will incorporate all other advance setting options.
The Mini Plug is available here: http://www.thesmartesthouse.com/products/zooz-z-wave-plus-mini-plug-zen07