Nope. Dragonborn are a widespread minority in the main area my game is set. They're much more common in Yuxia, far to the west, where dragons live. Whether this is a direct connection or not hsa never been examined (and I see no reason to have a firm answer regardless.)
Nothing to do with any game I would like to see run. It is a criticism of the dull uniformity and inflexibility of FAR too many D&D settings. ENWorld's Zeitgeist and Baker's Eberron are beautiful examples of what you can do when you reject merely doing things for staid conformity and instead actively pursue creative stuff. Other options that have not been taken, to the best of my knowledge, but which could be extremely interesting:
1. Greco-Roman sword-and-sandal setting. Tieflings could be re-interpreted as resurrected people marked by Hades, the dimanes (a play on the actual dii manes, the immortal dead). Dragonborn have several plausible mythic counterparts, such as the Spartoi ("sown ones", nothing to do with Sparta) that a couple different Greek heroes produced by sowing dragons' teeth, or as children of drakaina, the she-drakes who mythically sired lineages of kings or entire peoples through unions with heroes (e.g. the Scythians were held, in some myths, to be the offspring of Herakles and a drakaina), or as descendants of an Athens-like city because of figures like Erichthonios, who is often depicted as having a reptilian lower half.
2. Science-fantasy. This one's got a bazillion precedents. If we go far-future, just a reptilian race is extremely common in science fiction. If we go modern-fantasy, the "reptilian conspiracy" provides one angle, but for a kinder one, they could be the result of genetic manipulation. Tieflings fit naturally as the descendants of spirit-altered individuals or as a race that had contact with humanity in the distant past, leading to the myths about devils and demons. Etc.
3. Wuxia. TONS of stuff you can do here, there's so many East Asian or Southeast Asian myths and tropes you can draw on I couldn't even begin. Just off the top of my head, oni cover tieflings pretty much perfectly, and Journey to the West has a near-unending stream of animal-people, dragons that have or can assume human form (most benevolent, but some are antagonists!)
Instead, what do we get? The same damn tropes regurgitated over and over, flattened and flanderized from Tolkien without any real thought into what they actually do or are like. Hence why I take stuff about elves and dwarves to task. Elves and dwarves should be really weird. They aren't. In most cases, they're in exactly the same sorts of positions as humans, in exactly the same proportions, with no meaningful difference other than the occasional offhand comment about remembering a friend who's been dead for two centuries or meeting someone's great-granddaughter and commenting that they have their great-grandfather's eyes.