I don't really buy the argument, at the time the global human population was far too low to have the kind of negative effects we see today. It was under 500 million, if I'm remembering my timeline right.
Farming
What of it? For much less food, and with an intensity that might as well be nonexistant. There's just not a lot of environmental potential to be gained on a more wild Earth.
Do remember that the efficiency of agriculture in this era was vastly lower as well, requiring significantly more land for lower yields. The deforestation of Europe, for example, began long before the charcoal demand of the early industrial era; an estimated 30-35% of Europe's total land area transitioned from forest wilds to agricultural fields just between the 6th and the 14th centuries AD
[ref]. It doesn't seem entirely out of question for a similar argument for historical deforestation may be carried to the part of the world with the greatest population and the most intensive agricultural development based on the principles of state-led infrastructure development underpinning the entire concept of the hydraulic empire - China. Islands that exceeded their carrying capacity in Polynesia were effectively deforested, though I agree that this may be considered a fringe case due to their isolated location without external frontiers for expansion.
That said, it wasn't necessarily a positive effect. The sequestration of so much CO
2, even assuming their models were overstating the effects (I'll neglect Antarctic ice core samples that show actual atmospheric CO
2 levels; I'm not very familiar with the methodology there, and they seem to be used more often on geologic timescales) would have lowered global temperatures. It also may have been mitigated by other sources; just as the Little Ice Age did not correspond to a global decrease in atmospheric CO
2, Genghis Khan's little adventures took place at the tail end of and just after the Medieval Warm Period. That's obviously not to say that the two are related (if, for no other reason, than because the Medieval Warm Period's beginning and end are very fuzzily defined). It's simply that, as you already know, there's more to global temperatures than just atmospheric greenhouse gasses.
EDIT:
That said, it's worth noting that the study in question actually focused on four major depopulation incidents. Only the two most long-lasting ones, the Mongol invasions in Asia and the European colonization of the Americas, showed any sort of long-term effect in the models. The Black Death and the fall of the Ming Dynasty barely registered a blip; reforestation simply didn't overcome the emissions increase from decaying soil matter.