I guess it depends on what you consider drastic. Yes, rendering quadratic or cubic curves is more expensive than rendering line segments. However, the extent depends an the platform as well as the actual number of path segments.
E.g. on my Windows machine running yEd on Java 8, rendering an quadratic curve edge with n curve segments takes approximately as long as rendering a polyline edge with 4*n line segments. Running yEd with Java 23, rendering the same n curve segments takes approximately as long as rendering 3*n line segments.
Considering the fact that it takes about 1 second to render about 500000 quadratic curve segments on my machine, the above mentioned performance difference rarely matters in practice, because if you rendered that many segments at the same time even on a high DPI display you would not be able to discern individual segments anymore.
If your question is not about yEd, but one of the yFiles diagramming libraries, please contact yWorks support through the yWorks customer center.
