They definitely intended to keep it quiet. Himmler spoke directly about this in the Posen speech.

I also want to refer here very frankly to a very difficult matter. We can now very openly talk about this among ourselves, and yet we will never discuss this publicly. Just as we did not hesitate on 30 June 1934, to perform our duty as ordered and put comrades who had failed up against the wall and execute them, we also never spoke about it, nor will we ever speak about it. Let us thank God that we had within us enough self-evident fortitude never to discuss it among us, and we never talked about it. Every one of us was horrified, and yet every one clearly understood that we would do it next time, when the order is given and when it becomes necessary.

I am now referring to the evacuation of the Jews, to the extermination of the Jewish People. This is something that is easily said: 'The Jewish People will be exterminated', says every party member, 'this is very obvious, it is in our program — elimination of the Jews, extermination, a small matter.' And then they turn up, the upstanding 80 million Germans, and each one has his decent Jew. They say the others are all swines, but this particular one is a splendid Jew. But none has observed it, endured it. Most of you here know what it means when 100 corpses lie next to each other, when there are 500 or when there are 1,000. To have endured this and at the same time to have remained a decent person — with exceptions due to human weaknesses — has made us tough, and is a glorious chapter that has not and will not be spoken of. Because we know how difficult it would be for us if we still had Jews as secret saboteurs, agitators and rabble-rousers in every city, what with the bombings, with the burden and with the hardships of the war. If the Jews were still part of the German nation, we would most likely arrive now at the state we were at in 1916 and '17...