well no, the Nazis paid lip service to "workers" in general but literally got into bloody (as in armed paramilitary) conflicts with unions (Iron Front vs. SA) for years before the complete takeover of the government, after the takeover of the government almost all union organizers got sent to the concentration camps as political prisoners because "they were all Marxists", the Nazis then replaced the unions with the German Labor Front (DAF), an organization that existed to keep the worker in his place, going as far as to literally take money from the workers to pay for building new production lines.

so, no, they did not absorb the unions, and they definitely didn't back the unions, unless you call strike-breaking with a machine gun "backing"