00 Buck will not hurt a full choke gun, but as whenever a different load, or brand of load is fired in your gun, patterning the new load to determine it's pattern characteristics is beneficial. Similar loads from different manufacturers will pattern differently, and different loads from a single manufacturer will pattern differently when fired in the same barrel.
Steel shot is less compressible than lead shot, but I don't believe the gun would be "damaged" by using it, in that you're unlikely to experience a split barrel or something of that nature. More likely the choke will expand with use as the choke is swaged open, so your full choke gun will begin printing modified patterns, or worse, the pattern will be less dense and possibly donut, or begin printing in a linear fashion.