I'd read in "1493" by Charles Mann that some scientists and historians believe that the death of most of the population of the Americas and subsequent reforestation and lack of controlled burns across much of the continents was at least a partial cause in the worst part of the Little Ice Age, is there a scholarly consensus on this?
I don't know about a consensus, but a recent meta-analysis (study that combined data from many other studies) by Koch et al. concluded that the Great Dying accounted for around 90% death of Indigenous populations in the Americas, and that yes this caused a major uptake of atmospheric CO2. They show however that the Little Ice Age was already underway before the atmospheric CO2 levels dropped significantly, and that it thus did not cause the Little Ice Age. They do conclude that the Great Dying did contribute to the Little Ice Age, however, at the time when it was already coldest (basically the Great Dying made it worse).
This is a recent article and I haven't seen any critiques of it yet, so I cannot speak to its findings (I am not expert enough in the topic or methodology to really evaluate it, but it is in a major journal so that lends it some credibility). It is open access, too, so you can read it for free. It is full of stats and jargon, though.
No.
What Mann is claiming would have taken hundreds, perhaps thousands of years to occur on a geo-climactic scale, if it would have had any impact at all. It is a fringe theory that most scholars do not acknowledge.
Now, could it have been one of many contributing factors that led to the LIA? Possibly, but its impact would have been minimal. Keep in mind, the population of N. America was, at best, 4-5 million all told. Central and South America might have been double this. More of an impact, and would make more sense time-wise, would have been the impact of the Black Death. Killing off 30-50% of all Europe, plus deaths in the Middle East and where it came from out of China in the 14th century, would have had enough time to affect climate starting in the 17th century which is when most scholars peg the start of the coldest weather.
Larger factors would have been the Sun going into a down cycle, which it does regularly. Mix in some major volcanic eruptions and you have your LIA. One other thing to consider: The population and deforestation of the Americas, if it really had an impact, would have affected the climate of the ENTIRE WORLD.
The Little Ice Age was primarily a northern hemisphere event. Those in the south and around the tropics weren't nearly as effected, if at all.