Short answer: Yes.
"Sufficient" in this context means "enough to produce the specified result." Whether that result is desirable or not is irrelevant. Indeed, in some cases it could depend on point of view. Like, "XYZ Company had sufficient influence with the administration to push through a multi-million dollar government bailout." The result is positive from XYZ's point of view, not so positive from the taxpayers'.
I understand your problem. Some words imply a positive connotation. Like I recall when a news organization here in the U.S. announced a new policy that they would no longer say, "[whoever] claimed credit for the terrorist attack yesterday", but rather, "[whoever] claimed RESPONSIBILITY for the terrorist attack", on the reasoning that the word "credit" implies something positive. Of course the people launching such an attack presumably do see it as a positive accomplishment, so they are claiming "credit".
BTW, I'd say the logical opposite of "sufficient" is "insufficient". "Necessary" isn't really the opposite of "sufficient", but rather a different degree of the quantity under consideration. (Usually using "quantity" here in a metaphorical sense, like "Divisibility by 2 is a necessary but not a sufficient condition ...")