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I'm not fully understanding what you are asking, but you do not need a wired ethernet connection for either the device or your computer to do basic setup.
Typically, you would start with the omega functioning as an access point, and connect your computer via that. After doing setup that way and getting it connected to your wifi access point, you can then reconnect your computer to your normal wifi access point.
Then, unless your access point does client segregation (as some public ones do) you should be able to contact the omega from your computer by way of your wifi access point, much as you could share files between computers connected to it, print to a network printer connected to it, etc.
If you're correct about no LAN needed, that helps a bit. It did work fine with LAN. Now, do I need AP populated and Enabled (checked) in the Console for basic operation? I always know it's not working when router 192.168.0.103 disappears in Console, Settings. And wireless in laptop tray shows Omega-xxxx "No Internet, Secured" instead of "Connected, Secured". This is of right now. I use PuTTY for a terminal. It did work fine for a few weeks, then I did something? I know I'm jumping around. Better stop here.