I am going to say yes. As the they say, rust never sleeps.
The salt solution sits on the metal even if the boat is not in the water. I would not expect zincs in your situation to dissolve quickly, but they offer some protection. Easy to install and I bet there are already holes drilled for the install. For $10 you can protect your much more expensive trim tab hardware.
FYI, with stainless aluminum and salt water aluminum anodes might be a better choice than zinc.
My boat has zincs on the trim tabs and it sits on a trailer!
Zincs will not protect against normal corrosion, as in oxidation which can be caused by salt residue sitting on ferrous metal.
Zincs are meant to protect against galvanic corrosion, which occurs when two metals with dissimilar electrical potential are immersed in an electrolyte. The least noble metal, the anode, will begin to “give up” electrons to the more noble metal, essentially creating a battery. Zinc is one of the least noble metals, so as long as it has good electrical conductivity to the metal it’s meant to protect, it will give up it’s electrons and “corrode” away first, thereby protecting the metal it’s attached to.
If you remove the “electrolyte”, in this case the saltwater the trim tabs and whatever other metal are immersed in, there’s no connection between the metals and therefore no way for the electrons to flow. Therefore, no galvanic corrosion will take place and the zincs are unnecessary.
That said, for the cost of $20 each or so, it’s not a bad idea to install some. If you end up in a marina away from home for a couple days, or the lift breaks and the boat has to sit in the water, having the tabs protected won’t hurt. Also, since the tabs are usually dry, whatever zincs you install should last a very long time. But they’re only providing any type of protection if the tabs are immersed in water.
If you boat in saltwater, you’re just fine using zinc anodes. Aluminum anodes are only necessary if you’re using the boat in freshwater or very slightly brackish (mostly fresh) water. For your purposes, standard zincs will be fine and more affordable.