Iv played a lot of variants and to be honest they are fun. But do they help you improve? ( this is apart from antichess as it is a disgusting variant that destroys your standard chess)
I find that playing Crazyhouse helps me in regular chess by helping me visualize where I want to place my pieces. For instance i might see a nice hole in regular chess and i will think to myself: "If this were crazyhouse I would drop a knight there". From there I would look for ways to maneuver a knight there eventually.
I'm sure they give at least some improvement but if that improvement is as good as studying regular chess I doubt.