I'm sure it will be just as effective in stopping shark finning and keeping people from eating shark fin soup as marijuana laws were effective to stop people from smoking weed.
Actually it should be incredibly effective at least as far as massively reducing any shark fin consumption in California is concerned.
We're not talking about a dish that Chinese in the US prepare at home. Shark fin soup is basically exclusively served as fancy dish at Chinese restaurants and by caterers (who specialize in Chinese food) at banquets. It actually takes a significant amount of skill and time to really produce the dish properly. (As noted its all about the flavor of the broth and like rather than the fin itself.)
Any restaurant or caterer that tries to serve shark fin soup regardless would be potentially looking at some really nasty fines which should remove any economic incentive for risking it. (At most you would be looking at a restaurant or two that would risk quietly offering it to a extremely tiny number of people covertly, rather than the current situation where its relatively readily available.)
We're not talking about a situation like with marijuana where once you have possession of the material in question its easy enough to create a blunt to smoke it or otherwise do what you want with it.
You might still have a few people of Chinese ancestry go over to Nevada to buy a little bit of dried shark fin for general consumption due to its perceived medicinal value, (it actually doesn't do anything but possibly give you a bit of mercury poisoning) but if this actually became a noteworthy phenomenon that would put a huge amount of pressure on Nevada to ban the trade and sale of shark fins as well. (And this is not the primary way that shark fins are consumed regardless.)
The law certainly should basically stop sharks being caught for their fins in California waters. The fact fisherman can no longer sell their fins in California as well as Oregon and Washington State should also reduce the incentive to catch sharks commercially period (and even if they tried to sneak down to Mexico to sell them, shark fishing is going to be outright banned in Mexico soon.)
Its simply an extremely different situation than something like marijuana where enforcement can be such a problem.