I am going to say yes.
Depends a lot on the chef. My ol' chef used to ask me everyday "Still wanna be a chef?" Which is stupid question when you're still there, after a 16 hour day, at the end of a 70 hour week.
So yeah, the "Sink or Swim" method is quite popular from my own experience, usually, when they determine you're not entirely worthless, you'd usually get shown the ropes a bit more thoroughly (Boxing metaphor right there).
Personally though, I've always felt that if you're out of your league, or you don't know what you're doing, there's one piece of advice that never fails: Ask!
This is most commonly shared with new dishwashers, eg. the "People-won't-be-mad-if-you-ask-but-they-will-if-you-break-stuff" speech. And if you get told off for that, leave and don't look back. Find a place that's actually willing to teach you.
You'll get thrown in the deep end more then once, you'll get told off, scolded, yelled at and corrected more times then you can even imagine. Don't let it get to you, basically what every chef is telling you even when he's in your face, trying to trade spit with you, is "You fucked up, this is what you did wrong, please correct it next time" - It might not always come across as that, but it's basically nothing more.
I think we've all had days where we've come home and thought "Never again, first thing tomorrow I'm finding something else to do", few of us do. Be it the chef de cuisine that's having a bad day and taking it out over everybody else, or a lousy service where didn't prep enough, and find yourself having to do everything a la minute (My personal favorite, and something that always gets the juices flowing). We still get up every morning and labour through another day, because as ChefBoyarG said, the kitchen is your family, and you don't let your family down.
What you've experienced is not unusual, I don't recall hearing about someone in your situation (and age) being treated like that, but it does happen. Still, keep soldiering on, but be engaged, don't just take it lying down. Ask questions, do your best and communicate. If you still don't click, well - move on, don't look back. I've been to several places, where, for one reason or the other, I'd just never fit in. It does happen quite a lot in this industry, because you work so many hours, in tight spaces with each other, it's really important that you're comfortable with the tone in the kitchen and the other chefs. Otherwise you're never going to be happy. Don't worry to much about your first day, or even first week, or 3 weeks for that matter. You're going to acquire skills, and everything will get easier, and fast. Worry about the people, why did they do what they did - If it was with malice intent, or just to fill a spot, then think hard about if you want to stay there.
That's my two cents, the work environment trumps the actual work, especially in your situation, where you are still unsure as to what you've gotten yourself into.