Do Fallout and the Elder Scrolls Take Place in the Same Universe?

If you've played an Elder Scrolls game, you're probably familiar with the glowing Nirnroot plant, valued for its healing properties. If you're also playing Fallout 4 (who am I kidding, of course you are), you may have stumbled across an "experimental plant" that looks an awful lot like Nirnroot aboard an airship research station. 

I know what you're thinking, "it's just a reused asset," but, consider the notes from the scribe who discovered the plant in the Fallout universe: according to him, the plant emits a light that is a result of bioluminescence, not radiation, and makes him feel stronger when he drinks a tea made from the plant. Could they be the same plant?

It may very well be that these are totally different, but it's fun to speculate about a connection between these two universes.