For a HASL Finish PCB, Can Gold Plating be done
Can gold plating be done on top layer of PCB over this?


No.

HASL is an indiscriminate process that affects all exposed copper on the PCB.  Therefore you'd be trying to deposit gold onto a thin layer of uneven solder, which would cause all sorts of alignment problems for wirebonding.  Also the gold would simply float off molten HASL layer as soon as the (other) components were soldered down during reflow soldering.

Just have the entire PCB ENIG treated instead of HASL and then any further gold plating needed would have a solid and perfectly flat surface to bond to.

ENIG is not expensive, and is better than HASL in every way.