They clearly executed some of them, but the common depictions of the scale of executions and purpose of the camps doesn't make any sense.
My great-grandfather lived through the war and told me few interesting stories of the time. The way Jerries did it is that at the beginning, they put out a lot of "Workers Required in Germany!" poster ads in their freshly-conquered Poland, targeted towards its Jewish demographic. The funny part is that he and others would warn the people who took the bait that no, there's no work waiting for them there and they're gonna get robbed and killed. Jewish Reaction (a derivative of the Jewish Question, it seems)? Call them idiots who will miss out on a great opportunity to make bank.
They literally used FOMO pay2win strategy to kill millions of people.
'Pa then got forced to work in the actual camps later, so he had first-hand account of how the process went. Basically the numbnuts who arrived by train at the "worker's camp" were politely asked to hand all their belongings for "safekeeping" before being sent to the showers (for mass delousing, of course!). Adults and kids were separated for some reason, but in the end the naked kids got thrown through a hole in the ceiling to the adult shower right before turning Zyklon Ben. Then the corpses got whatever gold teeth they had pulled out, everything valuable was either send to Germany or sold and that's how they propped their economy at the start of the war.
The guy was of the "6 millions wasn't enough" disposition, so I doubt he'd have a reason to make any of this shit up. Also according to him Jews were kind of dicks and nobody liked them before Germans invaded. I've had other family member who saved one Itzhack from gas, his thanks for saving his ass was... a $10 cake, after the kike in question emigrated to the States and became a millionaire, literally mailed-in, didn't even bother to come here and shake his hand. Gee I wonder why everyone was so antisemitic in pre-war Europe?