Binding properties of turmeric Is turmeric known to have any binding properties? 

Wikipedia doesn't mention anything, and a google search only relates to iron binding properties of turmeric or similar health benefits.

A few days ago I made a curry (a Madras variant), and put the turmeric, as recommended by an Indian friend (I normally put it when creating the curry paste itself), in the latter stages of the cooking process. The curry was at that point not boiled down enough, but with the addition of the turmeric, the curry bound (binded?) in a similar way to adding flour. 

(Sneak side question if the answer is "No, it doesn't": Should You / Why Should You add the turmeric only in the latter stages?)
Turmeric is a rhizome that contains some starches. Those starches will hydrate and gelatinize like any other starch and thicken liquid. 

I don't know how its thickening power compares to other starches like flour or corn starch. This paper has a chart of vegetable starch sources that would imply that turmeric's starch content is fairly high at 76%

In many cuisines turmeric is used for color and flavor and isn't present in enough quantity to have this effect. As you have observed in Indian curries enough is used to thicken a sauce.

I add turmeric early when frying all the other spices to toast them. As with other fine powders, frying it early also makes it a bit easier to incorporate without clumps.

The only reason I can think of to add it later is if you are adjusting the flavor/thickness of the curry.