What the historical record shows. In the first year of its operation, the Trustees allowed payment of fees for less than 1% of 1366 class seats. And they made sure that those that did pay did not need the classes to earn a living. Charging tuition to students who need education for their livelihood is fundamentally against the founding principles of Cooper Union.
For details, see:
https://sites.google.com/site/tuitionatcooper/