Ages ago, I tried a kelp "noodle" called Sea Tangle. From my paleo point of view, (#1) kelp noodles look nothing like kelp and (#2) yes, sodium alginate is a gum extracted from the cell walls of algae, so it sounds natural, but extraction can mean many things, not all of them natural! We're not talking about a product that you could make in your kitchen if you were given a pile of the right kind of algae.
I avoid processed foods whose processing is a mystery to me. I mean, look at carrageenan: it used to be in everything, and it's still controversial for it's intestinal side effects.
If you ate algae, you'd be ingesting miniscule quantities of the unextracted gum that they make sodium alginate from. However, with a processed food containing the extracted gum, the amount of sodium alginate is much higher than you'd get if you ate the natural food. Who knows if that is good for you or not?