On the beach..a big yes. Can alternate running on the heavier sand and than closer to the shore line, where the sand is a little bit more packed. Gets the calves, as well as the front shin, very well. Also great way to build endurance, when 40 yard dashes are included in heavy sand. Not near any beach, than suggest running on grass. In either case, sand or grass, if on a hilly area so much the better.
Guy's who start martial arts/MMA/UFC type training are surprise with the amount of calluses than can be built up rather quickly. The original skin layer will peel off as the tougher level develops underneath. Blisters, may be a problem at first Could even run on your gym indoor tracks, starting with short distances at first, just to adapt to the harder surface.
I will usually squat and DL's barefooted. Seems to allow a better foot gripping for me.
Just my view: A lot of those big buck "training" shoes are over hyped just to grab your wallet. People do fall for that every day, sports shoes are a billion dollar business around the world.
Good Luck.