I am not a security professional, neither am I smart in this area. However, Cherlynn Low wrote an article that may help. It is called "How to Disable or Enable Cookies on Edge Browser." Here is the link: http://www.laptopmag.com/articles/disable-enable-cookies-edge-browser
Now, my answer to your question. If you are running Windows, then you can can bet that Microsoft is collecting data whenever you are connected to the internet. It may not be personally identifying information, but it does pull from your computer to keep it updated. That said, Edge is related to Microsoft, so while it may not directly "store" other browser information, the parent company does.
Case in point: If you are not using Edge, then it is not directly collecting cookie data. However, it can, but only if you allow it.