I dont believe OP. Back in college I drove my then 91 Corolla 3 speed automatic to Lake Mammoth via Hwy 395 for Physical Geography Field Study and it rode fine. Elevation is 7,800 ft. Yes it was very slow to drive up there even on L gear without A/C however I achieved that feat. I stayed on D mode 90% of the time which was running less than 50% of the speced 106 HP!
Like Toretto previously mentioned, It doesnt matter if you win by an inch or mile. Winning is winning Me vs doubt.