Given that the first statement is true, does the statement constitute
It depends how one understands the phrase "ad hominem". It is often simply used to mean an insult or abuse. I would say your statement likely is abusive, it sounds so. But that is to impute it with a certain intent. Common sense would hold it to be ad hominem, this is the usage now current on the Senate Floor of the U.S..
If it means an informal logical fallacy, concerning ruling out an argument, a priori, because of its source, that's wrong because you are stupid, ergo, all you say is wrong, then I would say this does not fit. Because as a matter of logic we can't bring in common sense, thus we must believe that the premise "you have not come up with a single logically coherent argument or counter-argument" is a fact. And not what it likely is, an insult or mere depreciation.
In the tradtion ad hominem was largely a phrase used to oppose eristic argumentation. Standing back and saying things without exposing oneself to persuasion. In the current usage, "adversarial" is what is opposed to ad hominem in the sense of the tradition. In Plato's Republic for instance, Socrates uses ad hominem argumentation to show Polemarchus that he did not truly have the opinion about Justice he believed himself to have. This was possible because he entered the argument in a friendly fashion, exposing his being to transformation. Of course, a defense attorney would be wrong to do that, since he would thereby abandon his duty to zealously defend his client, it is for the judge to enter the argument in that situation.