Kip Thorne thinks so. He was the scientific adviser for the movie Interstellar.
About the planets orbiting Gargantua he said the following:
This business of the enormous time differential between one of the planets orbiting very close to Gargantua and the flow of time back on Earth – the problem seemed to be that no planet could endure the resulting gravitational forces. This was something that even I thought was impossible, intuitively, until I went and slept on it and did a few hours of calculations. I came to the conclusion that in fact it is possible. The black hole needs to be spinning very fast, but is possible for the spin to be fast enough for a planet in the necessarily close, stable, circular orbit to not be ripped apart. I can’t fault anyone for saying, “Hey, that’s not possible,” without having first having the benefit of my book! Unless it’s someone who is very deep into general relativity and who I would’ve expected to go do the calculations!
Source: Parsing the Science of Interstellar with physicist Kip thorne
Thorne also wrote the book, The Science of Interstellar (2014). Copies available in all good bookstores and libraries. There is also a documentary about the movie's science which can be found here. I believe it is also an extra on the DVD.
Yes the science of Miller's Planet is plausible and possible. Kip Thorne is one of the top physicists working in the area of general relativity. You don't get better than that.