"If the Feds withdraw the billions spent through military contracting, research grants, support for college graduate funding, will the private industry pick up that cost?"

Only if all those private corporations in Silicon Valley and elsewhere like Elon Musk and Bob Iger, Lloyd Blankfein and Jeff Immelt are willing to work without Federal funding to "put their money where their mouth is" because of their deep personal concerns about the environment. 

But, being private corporations, I suspect they will expect measurable and quantifiable  results from the money they spend instead of just shoveling it into the troughs to flow into the university systems to never be seen again. 

 And the 'automatic' 10% off the top for 'administrative expenses' that most Federal Grants carry down level by level is also unlikely if they are spending their own money and not taxpayer money.