That sounds totally wrong to me. Agree (acordar/konkordi/être d'accord) and agree (concentir/konsenti/accepter) both sound very natural as the same word in english, but "disagree" only feels like the opposite of the first, whereas I'd say "decline" or "refuse" for the opposite of the latter.
"Disagree" as refusal sounds somehow haughty or preposterously off-the-charts formal. Like: Well, Jeeves, we seem to be at an impasse. I shan't throw away this hat, it is not hideous at all, and that is all I have to say on the matter.
