That makes no sense at all. That's like saying, I had spaghetti for dinner tonight, therefore everyone named John must have had spaghetti tonight.
In Italy, the monarchy was essentially the ruling house of a corner of Italy imposed over the whole country, whereas in Germany the Kaiser was also King of Prussia, by several orders of magnitude the most powerful part of the German Empire, so he was a much more significant figure in Germany than was the Italian King.
I do not think a personality cult would have been possible with a Kaiser in place. On top of that, the conservatives that backed Hitler would have no reason to if there was a monarch.
Italy was a constitutional monarchy and Mussolini came to power after his
"March on Rome." So to answer your question, yes, Hitler would have come to
power if Germany had been a constitutional monarchy.