Anxiety doesn't kill anyone, it's just damned unpleasant. Having said that, it can cause long term physiological problems if you overload yourself on it.
whether that will happen depends upon your own limits, no one here is going to know your limits.
You have to ask yourself another question however. If it's skydiving today, what will it be tomorrow? Do you want to set a precedent where you are dragged along on adventures you can't handle just to impress her? Or do you feel you can handle her adrenalin junkie lifestyle. If you are a naturally anxious person, what joy will you get out of living like that?
Of course if you are just trying to get into her knickers for a night, there's easier ways than jumping out of airplanes
it's called finding a different girl!
Finally bear in mind, that just cause you go skydiving, that doesn't mean she'll fall into your arms, you might end up doing it all for "The friendship zone". Worse still she might simply be manipulating you, because none of her friends would do it, and she'd dump you in a second if any one of them said yes.
Oh... and who's paying for this. If she's making you pay for it. RUN AWAY NOW. She's a user. On the other hand if she's paying, then it's a once a life time experience if you are brave enough to do it fantstic! Personally my trousers would be soaked with my own pee just stepping onto the plane, haha. I'll do alot to impress a girl, but floating down to earth on an oversized hanky isn't one of them lol.