Can quinoa be used as a soup thickener? The normal method for preparing quinoa is to boil water, drop the quinoa, wait until it "sprouts", then strain.

My question is about the last part: the straining.

Suppose you are making a soup (lentils, bean soup, ...) and it turns out there is too much water. You do not want to discard liquid, and you do not have patience for reducing by simmering. Is dropping quinoa in, partly as a method for thickening, reasonable?

In other words, what is undesirable about the water one normally boils quinoa in, for one to discard that water? Is there anything undesirable?

Update (Long comment to GdD's nice answer and pointer to saponin)

I didn't wait for an answer. I ran two experiments (on only myself). The result on both occasions is that quinoa is indeed an excellent soup thickener, on account of the amount of water it absorbs. But on both occasions the meal required a few (5 the first time, 2 the second) tablets of Tums to neutralize the stomach acidity (a rare occurence for the foolish volunteer in question). This doesn't establish that saponin, or even the quinoa, is the cause, but that's perfectly plausible. Incidentally, on both occasions the quinoa was carefully rinsed in a fine mesh strainer. That didn't help.
Cooking grains in soup is an effective way to thicken it, but quinoa is probably not the best choice. Quinoa has saponin in it, a bitter tasting phytochemical which has been known to irritate the stomach. Much of the quinoa sold has been presoaked to get rid of much of the saponin, but some may remain which is why you boil it separately and discard the water. If you put quinoa in the soup any traces of saponin could ruin or at least add off flavors to the dish. 

Rice or barley would be my first choice for that sort of thickening, they take longer but they don't impart much flavor to the food. Couscous is faster, but would give the soup a grainy texture. Giant couscous may work okay, I've never tried it in a soup myself.