No they didn’t.
On the one hand we have an out of context proposal letter from someone at some time referring to classified and unclassified documents. For all we know it was written before the final document arrangements had been made and there’s no indication the proposal was ever considered, let alone accepted.
On the other hand we have an official press release from a federal agency stating unambiguously that NARA took immediate and total control of all of Obama’s records, that the records in Chicago are not classified and are under NARA’s control, not the Obama Foundation’s, and that all the classified documents are under NARA’s control at a different, secure facility.
This is a click-bait story from people either too lazy to do basic research or too cynical to care when they can put out nonsense that they know people want to believe.
But the letter also makes clear that the documents had been transferred to NARA and were under NARA’s control.