While it won't hurt the gun, it will not be that accurate and will cause issues if you shoot brass cased ammo without cleaning the chamber first.
The steel case doesn't expand well like brass does. This means it doesn't seal the chamber and allows for carbon build-up in the chamber, thus making the chamber very slightly smaller/tighter. This is not a big issue if continuing to shoot steel cased ammo. If you shoot brass cased ammo without cleaning the chamber, there is a good chance brass ammo will get stuck in the chamber and require you to punch it out via a rod down the barrel.
My friend made this mistake, ONCE. Hasn't shot steel cased ammo since.
Also, you want to be sure to verify if the steel cased ammo has corrosive primers. If so, it will require a different cleaning method using soap and water and not powder/copper solvents.
