It's a grammatically correct sentence and your meaning would be clear to everyone. This is more common and well-known way to say the same thing : "He is an extraordinary genius who could turn the world upside-down."

"He is an extraordinary genius who CAN overturn the world." > This is not right . When you overturn something , the something is either cause to turn over ( the car overturned in the accident) or a reversal of a legal decision ( the High Court overturned the guilty verdict) "He is an extraordinary genius who CAN revolutionise the world." Or , completely transform / change the world . Upside down is not appropriate . it means "in or into total disorder or confusion."

Kenny's answer is unhelpful. "upside down" is absolutely correct in this case. Note that Jen from the USA was in complete agreement with me. Kenny, please stop your corrections - I frequently see mistakes from you that indicate that you do not have a native level of English. You have even tried to correct a more advanced learner than yourself who put you in your place quite strongly. Now you are saying that my correction - which was completely endorsed by an American tutor - is wrong! You are saying that two native speakers got it wrong. This is confusing for learners and a waste of everyone's time. Please stop this.

You're correct.

Yes, that expression is correct.