Uhura can work because she'd be a fourth-year Cadet around 2259 and about 21 years old. It's forced but there are only seven more years before she's a Lieutenant on the bridge of the same ship. A Khan descendant, yeah, that's pushing the stupid envelope.
It's science fiction. Anything can work. That doesn't mean it's not unlikely to the point of pandering to the fandom for nostalgia views and suspension of disbelief breaking.