I don't think an easy answer for your question exists.
My "by the book" answer would be this: "No"; I think you would need to have a WPS qualified by PQR to weld over the galvanizing. Second you would need to test your welders using the WPS with the appropriate galvanized base metal.
My "real world" answer would start with the question of why you need to weld over the galvanized coating. If the component is a structural load bearing component, no welding unless the galvanizing is completely removed from the weld and within 2 to 3 inches of the weld.
If it isn't a load bearing part (an example is attaching a grating system to a steel deck), I would solicit the engineer to explain the use of a 6010 or 6011 to burn through the galvanizing, achieivng an acceptable weld for the application. Most of the time, the engineers are open to this discussion. It may help to run a mock up showing how it will look in practice.
Many times things like cable tray clips or tubing clips are welded to steel that has been galvanized. In those cases if you are the QC Inspector you can be as hard as you want in application of the code. You are safe in saying it isn't appropriate, but the reality is it might not make enough of a real difference to warrant rejecting the welds.
Sometimes it's an easy call and sometimes it's not.
Charles.
I believe that you should never weld galvanized steel. Even in unfortunate cases where previosuly galvanized material must be either field or repair welded, it is necessary to COMPLETELY remove the coating from the weld-affected area in order to produce a sound weld. Best method for removing coating is by grinding. After welding, the area should be re-coated with zinc-rich paint. Attempting to weld galvanized steel without first removing the coating will introduce undesireable, contaminating components in the weld metal. In addition, the burn-off fumes are HIGHLY toxic. So in my opinion, the ONLY way to weld that material is to return it to a bare state in which case, the A36 qualification that your questioning should be applicable.