Does a MacBook Pro 13 inch Retina late 2013 work with an early 2013 Retina display? As far as I know just the webcam cables are different. Does that mean that the display works just without the webcam (which I don't need)?
Browse ifixit.com and you can see ifixit's part numbers for these two 13" Retina MacBook Pro machines.
The "Display LVDS cables" on the two MacBooks carry the same ifixit part numbers. The two models' "Screen Assemblies," however, show different ifixit part numbers. Because the screen part numbers are different, I think the answer to your question is "Probably not."
If I were in your shoes and really wanted to resurrect my MacBook Pro, I'd look for the specific part that fits your model MacBook Pro, or a used MacBook Pro of the same model from which you could remove and reuse its screen.