Q: Wireless OS X Server Possible Out of the Box?

I'll assume you're pondering connecting a web server, mail server or other services to the Internet.  Not operating the server entirely locally.

Your local network connection is less interesting than the tier of service from your ISP — OS X Server much prefers static IP when providing specific services on the open Internet — and the details and particular configuration capabilities of your ISP-provided box.

A conversion of this box or of a replacement box to one that can provide a so-called "bridged" connection is much preferred here, and — yes — a wired connection is preferred as Wi-Fi can be flaky secondary to interference.    But that's not necessary, of the ISP device is sufficiently programmable.

Unfortunately for those folks running servers, ISPs tend to pick dumb, cheap, simple to configure devices — this for very good reason, as those are much easier to support and maintain.   If the ISP can convert the device to "bridged" mode, you can install a more capable gateway-firewall-NAT box and/or your own Wi-Fi and other services.

Also, Wi-Fi is particularly flaky in built-up area, as new Wi-FI routers and access points can appear at any time, and existing ones can be reconfigured at random.   This can hose your server connection, just as it can hose a client connection.

Details of the specific model of ISP gateway-firewall-router-WiFi-NAT box will help somebody research that.   Or by reading the ISP documentation and starting to explore the port-forwarding capabilities of that particular device yourself, of course.