Did him and Franco Peg each other is the question
No. If you spend any time at all learning psychology you would instantly recognize Arnold as a true sociopath, not a narcissist. He seems ego driven, this is not so. He cultivated that persona in order to achieve his life's GOALS. If you listen to him speak about success his #1 secret to success is that he set goals early on in life and then achieved them.
Bodybuilding has always been funded by homosexuals, if you watch enough vids of Arnold no doubt you'll wonder how straight he really was. I can assure you, he was not gay or bisexual. He grew up in post ww2 Austria, born to a police officer in a conservative village. He said himself women were a means to an end, bioligic drive that I think he didn't care for as much because it took time away from achieving life's goals