Best to check with the manufacturer. Best practice with any rifle is to check the barrel markings and use the caliber stamped on the barrel. A barrel chambered for 5.56 NATO can fire its parent cartridge, the .223 Remington. In most cases a barrel chambered in .223 Remington can not fire a 5.56 NATO cartridge.
Why? 5.56 NATO generates more pressure than .223 Remington. A .223 Remington has a different chamber leade than a 5.56 NATO chamber leade.
There are some instances such as Cyphertext mentioned where the barrel is stamped .223 and the manufacturer explicitly states their .223 stamped barrel can fire 5.56 NATO. This would be the only instance where I personally would do this. I always err on the side of caution.
To add another bit of info, a .223 Wylde which is a .223/5.56 hybrid chamber that can fire both.
http://en.wikipedia.org/wiki/.223_Wylde