Internally, the package will call your function, so, it cannot add magic speedup to that.
If your vectors are small, you might want to use StaticArrays, if your vectors are large, you should probably pre-allocate the result and make sure your function works also in-place.
So, in principle it is just better organization of your code. However, if the new type gives you access
to useful helpers, that could then lead to speedup. The LinearOperators.jl package is focused a bit on applications optimisation, e.g. you have special types such as LBFGSOperator.
There is also a similar package which has a bit closer links to iterative solvers, maybe that is better suited for your case: Home · LinearMaps.jl
Here you can see how creating a LinearMap type allows you to insert your linear map into iterative
solvers and that can be very useful to test your own method or to directly use faster solvers for your problem without having to implement them.