Forgive me if I'm not remyem being correctly but I studied the time period a around and after La Conquista a few times in college and the sense I got was that while there were high death rates due to illness, war, maltreatment and other issues the Americas didn't just end up devoid of life and technology. Rather, slowly the Spanish and Portuguese moved to the new world and a few things happened to the population. The minority conquerors (many of them bachelors) mixed with the native populations which gave rise to the mestizo class of peoples. In addition, African slaves were brought over and they mixed with the natives and Spanish/Portuguese alike. As time moves on, a very complicated racial structure develops that still has effects on Latin identity in the new world today.

So while there was a vastly diminished native population, the conquerors filled in with their people, mixed with the natives and brought African slaves who also mixed in. It is also my understanding that old world tech and customs made their way over and were very much forced on all in the new world.

In short, while the conquistadors had a very substantial effect on new world populations, customs and technology, there wasn't a long enough void for it to enter into 'life after people' territory.