No, that is not correct. If you read the concordat (it is online) you will find that it gave 'freedom of worship' to Catholics and it banned clergy from political office (sep. of church and state). Which of course did not happen as Catholic political groups were shut down (adherents ended up in the camps) and priests and bishops were imprisoned and executed. In 1933 the Church viewed the Nazi party as a barrier to the spread of communism but quickly found out the truth and the pope issued "Mit brennender Sorge" ("With Burning Anxiety" - a statement condemning what was going on in Germany) and the Nazis started a concerted attack on the Church in Germany.
The 'Currency' and 'Immorality' trials that peaked in 1935 and 1936, resulted in the imprisonment and fining of hundreds of clergy. Because the various Protestant Churches were split amongst themselves and so easier to control, the 'Reich Church' was created - a national Church with a Bible and 'Mein Kampf' on the altar.
Vatican saw Hitlers ways from the early 30's.
and still threw in with him....and so did the Catholic Church in other axis alligned or occupied countries who cozied up to Fascism.
Photos in my previous post say a Thousand words
you can deny my typing.....but you can't deny the Photo's