Very few people seem to have tried this and it would be good to read some reports if it makes any practical difference.
There are a few potential drawbacks:
Any weight on the shank significantly decreases the performance of most modern anchors. It does not take much weight to have a noticeable effect on the centre of gravity. This is the main reason why many modern anchors use hi-tensile
steel in the shank rather than a slightly thicker (and therefore equaly strong) section of mild
steel.
Anchors need to bury to
work well. If you look at the lower edge of shank on the Vulcan in the
photo you can see that it is tapered for this reason. The anchor can become completely buried in some conditions. An anode is going to reduce the
depth of bury, but how much of a practical effect on the holding is difficult to predict.
I would not use a zinc anode. Because there are different mixes of zinc it is possible the anode would actually be cathodic to the zinc in the galvanising. This would corrode the galvanising rather than providing protection. An aluminium anode would be better, and this also minimises the weight problem.
I would also suggest two small anodes on either side of the shank rather than a larger anode on one side. Anchors need to be symetrical in terms of weight and particularly in refrence to drag through the substrate. Without this they will struggle to orient themselves upright.