I see brides putting the veil on upside down/backwards quite often when we're at bridal shows (we have a very fun and popular booth for dress-up!) or when I'm assisting wedding photographers (something I do for fun, and to learn more about photography). If you put the veil on the wrong way, you'll end up seeing the gathering on the comb, not the nice, finished side. You'll also end up with the wrong layer on top on a multi-layer veil, and it just doesn't look right. But worst of all, you'll be putting the veil in in a perilous way, one leaving you vulnerable to the comb being pulled out with every exuberant hug (and you'll get a lot of those!)
Just remember: the teeth of the comb should always point either down or back. Never toward your face, never toward the sky. Even if you're wearing the comb under your up-do. If you're wearing your veil at the back of your head, it can be tremendously helpful to take the veil with you to the salon and let the stylist place the veil.
If you're wearing an extremely low chignon, and there simply won't be any room beneath the hair to place the veil, a far better option than wearing the veil upside down is using bridal loops rather than a metal comb. Bridal loops aren't quite as secure, but your veil will look better and will be more secure than if you try to wear your veil backwards.