Can a plastic blade be sharp?

Yes            

The cutting edges of these devices are made out of some hard plastic. This material is tough to the point that it effectively slices through delicate vegetables without you giving any extra pressing factor. ... Further, the creators can without much of a stretch handle this plastic material to make fine cutting, sharp teeth.

Plastic is just a general term.  There are literally thousands of variations from milk jugs to material you could shave with.  All this because we went to the moon.  Hundreds of thousands of folks are alive and lived longer because of the new plastics used in medical equipment and production of drugs.

Yes, some plastics can have a Very sharp edge for a short while but can't be re-sharpned very easily.

I do not think you can make sharp. Sharpness depends on the surface area of contact. You can make metal edged very sharp. If you do the same for plastics then the edges will bend and increase the area of contact. Thereby, they reduce the sharpness. The plastic can not be made sharp.

Define sharp...

Yes, but not for very long

Yes.