Will this type of welding be strong enough to withstand Southern California winds?
As long as the weld has made good penetration into the two metal surfaces you should be fine. From my experience the only way the weld would fail is through metal fatigue which involves a consistent flexing or bending of the metal. I don't see this happening (or it is highly unlikely) given that the steel posts (they appear to be C channel or columns) will be tied together by the horizontal IPE boards making it a rigid structure. You would probably get more failure to the welds from seismic movement than from sheer wind force.