I am pretty sure the answer is no, but I have only inked about two pictures so far, and I can't remember doing any burnishing before the color fill, but I thought I would ask anyway!
Generally any time you add something on top of a burnished paper, you are adding another microscopic Himalayas which you need to flatten down to the Netherlands so that you can add the next layer! Layers can be single lines - no need to burnish after every single brushstroke of course, but when you've gone without burnishing for a while then have a feel and if it's no longer smooth, burnish. After inking in and before colour fill you may have lots of tiny hills which need landscaping before applying paint yes! It's also about habit forming, and to do it after the inking is a good practice.
Generally any time you add something on top of a burnished paper, you are adding another microscopic Himalayas which you need to flatten down to the Netherlands so that you can add the next layer! Layers can be single lines - no need to burnish after every single brushstroke of course, but when you've gone without burnishing for a while then have a feel and if it's no longer smooth, burnish. After inking in and before colour fill you may have lots of tiny hills which need landscaping before applying paint yes! It's also about habit forming, and to do it after the inking is a good practice.