I would be careful, but note that the US does not have exit passport controls. They couldn't even tell if you left or overstayed your visit.

My situation is not exactly the same as I am a dual citizen of US and the Netherlands - when leaving the US (for travel to EU/Schengen) I put my NL passport details in the API, then change that to the US details before returning. As well, my name is exactly the same on both passports.

[Added later]Not sure about my statement about not having exit controls after some googling, suggestion is that the airline provides the data to USCIS. So my advice would be to ensure you use the German passport when leaving as well