I assume it would be possible, though I don't know if the effect will be what you want. Places that do custom dye-subs will print samples for you, so you should probably do that if you really want to know how it'll look.
That said, if you print onto blue fabric, you won't be able to have the white spider design printed, as the dye-sub process doesn't have white ink. Any white/light parts of a dye-sub design need to be printed on white fabric.
While you could have the suit printed without the white spider, you'd have to apply it later, either by white paint or by a white fabric or appliqué of some kind laid on top of the suit.
But if you opt not to have the spider printed as part of the suit, and don't want any other details printed, then it seems kind of unnecessary to have it dye-sub printed. It'll be basically just a black suit, which you can find a basic black spandex for cheaper than the cost of a custom made dye-sub suit.