Perfectly safe but remember to upshift as it will stay in that gear and you will bounce it off the rev limiter. Also remember to put the car into D or 1 as it doesn't like to start in 2nd or 3rd. I always forget and try to start in 3rd and wonder why it isn't going so good.
I don't quite understand: You have an automatic transmission (thread title)? Without paddle shifter? I know no NSX with paddle shifter. The auto transmission seeks the gears itself or you can choose them at the steering wheel in a somewhat manual mode.
i have an automatic without the gear selector on the steering wheel and was wondering if it would damage the transmission to shift through the gears using the gear slector (p, r, n, d, 3, 2, 1) , shifting from 1st to 2nd to 3rd to drive.