No, but gotta tellya, either Peter had a great sense of awareness, or humor, because he knew Babylon when he saw it, lol
Yes, Peter recognized that pagan Rome needed to hear the message of Christ crucified, and was himself martyred there for his efforts.
And there is absolutely no proof whatsoever, that Peter ever went to Rome, was beheaded, and or crucified upside down. Scripture does not speak of any of this.