You can see correctly when wearing contact lenses inside out. I know because I did it this morning! I have recently changed to a new type of lens, and the new ones are much more flimsy than my previous ones, and no matter how many times I turn it inside out and hold it up on my finger and look at the curve, I just can't tell if it's inside out or not!
The only way I can tell if it's inside out or not is after a couple of hours of wear - it feels a little uncomfortable and irritates my eye. I always carry a little bottle of solution around with me, so I just find a mirror, take out the lens, give it a bit of a clean and turn it around! And then it's always fine after that.
So basically, other than a little bit of irritation, my vision is not affected if the lens is inside out!
Try to remember that a lens is usually sitting inside-up in its unopened container, so if you make sure you take it out the right way then there should be no problems!