When?
It also depends upon how long before 1492 the ship crew lands there, whether it's from a relatively advanced country or a backwater, whether there are some skilled people or mainly unskilled people on board, and more.
With a highly advanced and skilled medieval people (think of Spanish Muslims or an exceptional crew from around the North Sea or the British Channel), America could have gone through some Eurasian diseases and developed pretty much on par with Europe.
Agriculture was starting to develop in some southern parts. It would probably spread much faster with some agricultural knowledge from Europe, thus leading to a population explosion.
The Spanish arriving in 1492 would still be superior, but not enough to achieve what they did IOTL. The Euramericans would quickly learn to produce guns, gun powder, larger ships, and so on. Even with another catastrophic wave of disease running through the Americas again, America would not be considerably weakened - it might actually be a motor for development, as was the plague for Europe.
Europe had a lot of difficulties with the original inhabitants of America. A more advanced and numerous people would likely be more of a problem. So there would probably only be a few Spanish and Portuguese colonies in the south and in the Carribean (areas to which the knowledge of the shipwrecked Europeans did not progress), while northern parts of America go through difficult but more or less independent phases, similar to China.
As with China and some more independent minded countries resisting colonialism, trade would probably quickly be established, colonies might come up and go down, and so on. America would be introduced to modern developments in Europe, like different economic policies, different government systems, and so on.
Spain and Portugal would still loose grand power status, which would probably mean independence for the south as IOTL, or conquest by the north.
All in all, I'd see an America strong enough to stay independent, but a backwater even today, even with all the ressources - similar to Africa or India, though probably on a higher or lower level.