Yes, you can. There's no inherent hardware limitation preventing you from doing that and all common OSes will assign any IP address you want to interfaces, with the possible exception of multicast addresses, 0.0.0.0, and 255.255.255.255. Some network devices like consumer-grade routers or DSL modems may prevent you from doing this via the firmware.
You can do anything you want on your own LAN.
If you ever expect to connect these systems to an Internet-facing router, though, then you could experience the following issues if you don't stick with private IP ranges:
- Traffic destined for another host may leak out on to the Internet.
- You might want to get to the IANA-assigned host on that IP and may not be able to do it if it's an internal host.
- If you aren't the only one mantaining this network, you could horribly confuse someone who is doing troubleshooting.
ISPs shouldn't let private-IP ranges out onto the public Internet. This convention is why people usually use them when indicated.