That would be one unfortunate consequence with this PoD. I'm not entirely sure Stalin would do that, though. It'd be very difficult to capture Hitler alive — essentially, the decision is with Hitler, because you can always keep a cyanide capsule in your mouth or set off a grenade at the last minute. Faced with the death of Hitler as an accomplished fact, Stalin may decide it's better from a propaganda perspective to celebrate the event. Or he might want to cover it up. That decision is with Stalin.
For all the talk of neo-Nazis being emboldened by Hitler's last stand, I think it's probable that a KIA Führer ends up less of a legend. There may be film of the event, and there will be photos of the corpse. Images of people who have died violently are ghastly and hard to forget. They remind us that humans, even ones who think they were chosen by Providence to lead the German Volk, are flesh and blood. If there are photos of Hitler's corpse, then seeing him give those impassioned speeches in the 30s will remind people that he ended up dead in a gutter in Berlin, with whatever catastrophic injuries caused his death. Even just seeing his body without a uniform has a similar effect — Hitler, in life, was preoccupied by that, and would permit his doctors to see only as much of his body as was absolutely necessary.
