I think the numbers would probably go down, because there would be no way to get the money back. I'm against raising revenue by lowering charitable deductions. I think we should keep this part of the system the way it is.
Considering corporations around the world are systematically destroying our environment, I have no faith that they would continue to donate at current levels if there is no tax incentive. It's all about PR. Make your charitable contribution from .5% of your profits, and since your profits are so huge it looks like you are being generous.
The whole system needs to be restructured, and this does not include lowering the tax burden of corporations and raising the tax burden of middle and lower class Americans by "eliminating deductions," which are rarely ever specifically laid out.