Does a patina on a knife prevent rust?
In this case, the use of the word patina is a little misleading. Patina refers to the oxidation film on bronze or aged polish. I assume that you mean that the knife is coated with a substance.

First, when steel oxidizes, the iron oxide that forms does not stick well and will flake off the surface. This would not be useful for a knife since the edge will become dull quickly.

Second, if the knife is made with stainless steel, it does not need to be coated to prevent rust, only keep reasonably dry. Some stainless steel will actually rust since it was not properly formulated. Very few knifes are made of other metals since stainless steel is reasonably cheap.