If there had been no Lieutenant Uhura, the United States space program would've stayed the domain of white men for considerably longer.
... Unlikely, at best.
Yes, I know all about Nichelle Nichols being asked by NASA
to encourage minorities and women to join NASA. A job she
excelled at and I have read interviews with some women (plural) who made it as astronauts, crediting her. That is a fact ...
It's also a fact that STAR TREK was not needed to inspire the military to integrate minorities between WW2 and Korea. STAR TREK was not required to inspire MLK on his mission for equality. And NASA, like the military, wanted equality in its own ranks.
Now, using STAR TREK was a help, yes, in getting people's attention, especially children. But if NASA wasn't so aweful at Public Relations on its own, it wouldn't need celebrities to help push it. NASA made even the moon landings look like an expensive outing to collect rocks.
And if there hadn't been STAR TREK, some Amelia Earhart wannabe would've been the standard NASA's targeted group would've rallied around. STAR TREK was never known for its "cool" factor, until the reboot. Let's not pretend about that. Yes, the show's been popular for decades, but during most of that time, fans were branded as friendless geeks, living in their parents' basement, going to work in their "uniform" and making everyone call them "commander."