No. Physically, people are fully formed by age 21, though the are still developing in their teens. Drinking during the teen years is not a good idea, if done in any sizeable amount. After 21, though, it will not do significant harm unless abused. Part of that development during the teen years reduces the likelihood of developing an addiction, unless exposed in quantity.
What your question means and what you didn't explicity say is whether Americans can handle drinking at 18, 19, 20, or some other age under 21.
The answer here is a simple no, but. It's obvious that on a whole, there are far too many underage drinkers causing problems -- what reason do we have to suspect that they would instantly be responsible and no more harmful than the people 21+ if they were allowed to drink at a bar, or purchase booze at a store? There is no evidence that our current generation has such capability (I am 22, so I understand how high school and college freshman handle drinking now).
But... I think a LARGE reason that underage drinkers take their drinking to such extremes is because of a few reasons. The first is that it is illegal, and thus they want to know why. The second is that nobody actually teaches you how to drink in this country. Everyone learns about drinking on the spot, with a drink in hand and a couple friends at a party that don't know what they're doing either. It is little surprise that these kids would be through a bottle of vodka before long, passed out on the lawn, bent over into a telephone pole puking on themselves.
No, I don't think 21 is too young. I think that American parents should teach their children about drinking before they learn for themselves. As a whole, US parents do very very little parenting. They have an attitude that the schools should do it for them, and that government should help regulate what they kids do, see, watch, hear, and learn. I'm willing to bet if instead of making alcohol out to be a pure evil, parents told their kids why people drink, what they drink, and let them try some of their drinks in their early teens it would be different. Instead of chugging a bottle of vodka at 17, they would be sipping a beer at 14/15 with their parents. They won't get destroyed, and they'll understand control. W/e, just my 2 cents.