Stropping dresses the edge and is one of the few things in straight use that has been considered mandatory since the earliest use of a straight. Think of using a quality chefs knife and taking it to a steel before each use.

It does make a difference however in your case as there might be other issues like your edge itself. Stropping produces smoothness and comfort. if your razor is balking at shaving after 2 shaves stropping isn't your problem.