Considering his fascination with the roman empire. I know he wanted to build gigantic buildings in Berlin, he hated Jews enough to create a Gladiator like theater. But maybe the Germans didn't?
Perhaps it's a bit of a odd question, or i have just watched 'gladiator' too recently, this question has me fascinated for the last couple of days though.
In terms of fights to the death? No. You seem to have the idea that the Nazis wanted to make a spectacle out of the murder of the Jews. They certainly wanted to make a spectacle out of their opposition to the "Jewish conspiracy" - for example, the widely publicised boycott of Jewish-owned businesses - but the idea of having gladiatorial fights was never considered.
However, Albert Speer's plans for the gigantic buildings you mention included a stadium that would seat 405,000 people, in addition to two enormous parade grounds - to be named the Zeppelin Field and (appropriately enough) the Mars Field. These could be considered akin to the Colosseum in that they would be enormous public spaces for shows, contests and other, similar events.
Source: R.J. Evans, The Third Reich in Power, Evans himself citing several primary sources including Speer's memoirs.