Not if they find an inane one. The question is whether the parallel is substantive, relevant, and historically resonant with the Nazi template cited.
In June, 1934, Hitler hadn't killed masses of people yet. Until the "night of the long knives" (the slaughter of the SA command staff around Ernst Roehm on June 30, 1934), it's arguable that the Nazis hadn't killed anybody. It would not be unfair to call someone who'd replicated Hitler's curriculum vitae and political resume to that point a Nazi, since the Hitler of 1934 was, in fact, a Nazi.
By your rule of thumb, we shouldn't call Hitler a Nazi until and unless he had accepted the Wannsee Protocol for the destruction of European Jewry. But his and many other Germans' and Austrians' embrace of antisemitic, anti-Gypsy, anti-Slavic Pan-Germanism was already generations old, dating back to the earliest articulation of Pan-Germanism in the 1880's.
Hitler didn't intervene in the Spanish Civil War until the autumn of 1936, didn't occupy Czechoslovakia and Austria until 1938. At what point did he, under your working concept of what and who deserves the epithet of "Nazi", become a "Nazi"?
The whole point of calling someone a Nazi is to point out that he and his party are replicating the Nazi career to ruin and death, before we get to the point that someone must inevitably experience the denouement.
You make good arguments. My disagreement comes from not just a political viewpoint, but also from a language perspective. I'll say it again --- if Bush is Hitler, there is nothing left to describe Hitler. To me, when those comparisons are made, it lessens the impact on people of the incredible evil that was Hitler.