Nope. You just need his blood or something. Basically you just need his dna and not his whole body...
I firmly believe, and I think most would agree, that you need the body secured in some sort of shape in order to summon it.
The only exception is animal summons, where you sign a pre-existing blood contract with all the animals of that kingdom.
But back to the argument. Orochimaru noticed the summoning of the 1st, the 2nd, and then he said something like "I must stop the 3rd/4th at all costs." Based on what we know, the 4th Kazekage wasn't on the same level as the 4th Hokage. The 3rd knew that the 4th was stronger than him, or at least that he couldn't fight the 4th, along with 2 other hokage. And because of Orochi's personality, It is fair to assume that he was summoning the 3 previous Hokages to fight his former sensei.
It has to be Minato..