Yes, of course, as long as the original flavor and reflection of the time of what came to be the first three books were written is not lost!
Not sure why you consider that important. It's being made for a modern audience, and it's set thousands of years in the future. Gearing it for 1950s nostalgia would be a recipe for disaster, since the majority of the target audience members would be new to the work and wouldn't understand why something set so far in the future felt like some creaky old 1950s story. As I said before, the established fanbase for something like this is far, far too small to be the sole target audience. The goal of a screen adaptation is to introduce the work to an entirely new, much larger audience, some of whom will then be curious enough to seek out the original books.
Besides, you will find very, very few science fiction writers who want their work to feel dated and tied to a specific decade. What we want to do is convey a sense of the future. We can't avoid filtering our futurism through the biases and limitations of our own time, but that's a bug, not a feature. Given the chance to go back decades later and revise our work, the dated, period aspects would almost always be the first parts we'd want to get rid of. Because they represent the failure of our attempt to create a plausible future. That's why Asimov's later Foundation novels weren't written as pastiches of his 1950s style. The dated elements were not the parts he would've wanted to preserve.
And really, what is there about 1950s prose-SF sensibilities that's worth preserving? The rampant sexism? The exclusion of nonwhite characters? The giant computers based on vacuum tubes and punch cards?