Yes.
You’ll always want to boil, chemically treat or filter the water, but it is drinkable over short periods. The taste is poor due to its very high mineral content, but it’s not as bad as often feared. The taste is chalky, slightly salty, with the occasional sulfurous bite, depending on where you draw it from. Clear water can be found upstream from Blue Spring that looks more palatable, but the taste is the same as the turquoise stuff.
Is it safe to drink the Little Colorado River water? Ask a scientist – I’m honestly not sure. Several radioactive studies have been performed over the years (in addition to latent radioactivity there was a significant uranium tailing spill in one of the Little Colorado’s tributaries in the 1970s) but I have not been able to retrieve the data from USGS yet.
On longer trips when we’ve drunk from the river for several consecutive days it does have a considerable “drying” effect – probably due to the high salt and mineral content. By the third or fourth morning, it’s not uncommon to see every member of the group wake up with puffy eyes and faces. The effect goes away once you mobilize and get the blood going a bit.
I don’t believe it would be possible (or advisable) to sustain human life for extended periods on Little Colorado river water due to its slow desiccating effect on the body. Short term, it’s entirely do-able.
Under heavy flows, you’ll have large volumes of silt and sediment to deal with, as well.
The first perennial source of water in the gorge is nearly halfway down, a mile or two upstream from where Horse Trail joins canyon bottom.