I'm not in favor of the bill, but a warrant is still required (at least for domestic stuff).
https://www.youtube.com/watch?v=oYNXVgYhPOc&feature=emb_logo
General Alexander was very precise in his choice of words when he repeatedly stated "in the United States". What went unasked was whether these operations take-place against U.S. citizens outside of the borders of the United States.
So long as the courts entertain the loophole, it's more accurate to say that searches do not require a warrant than to say that they do.