I agree that welding of galvanized steel is done all the time. On critical welds one needs to be assured that the galvanizing is removed. Zinc is very ductile material and will smear over the surface. To check to see if it is removed heat the cleaned(sic) steel to around 500 F, the steel will turn brownish while any galvanizing will be silver in color.
Zinc forms brittle intermetallic compound with iron. Cross section some welds on galvanized steel, polish the surface using kerosne as the lubricate and etch with a Cro3 solution. It is not uncommon to find zinc pipes starting at the root of fillet welds.
As one know along the the is aone can observe the HAZ in the steel. There is aloso a HAZ in the galvanizing. Depending on the galvanizing alloy strange intermettalic compound can form (many very brittle) and could cause solid metal embrittlement of the steel. This is time at temperature dependent, therefore watch interpass temperatures, keep as low as possible.
Commercial galvanizing is generally 98% zinc, 2% of aluminum, tin, bismuth, lead, nickel. Several low melting temperature eutectoids can form that could wet the columnar type grain boundaries in the weld's solidifcation zone.
Because of the galvanize coating common low cost NDE methods to locate discontinuities do not exist, with the exception for the limited use AC Dry Yoke magnet particle inspection. ACFM (AC Field Measurement), though realtively new (ASTM standard approved last year)and fairly expensive can detect dicontinuites beneath coating at realtive quick speeds and provide a permanent record.