Yes. Just because they use the same base source code doesn't mean each version doesn't have differences. This could be temporary such as an enhancement made in Edge that hasn't been merged back into Chromium yet or a fix in Chrome that hasn't been merged into the current version of Edge. You need to test both.
I think you'll find that universally any web app developer will test all browsers that their app is designed to support, including the minimal versions of said browsers. I don't know that there is any guidelines published by MS because it is implied but I could be wrong.