Some stuff online suggests that it cannot and that it settles out of any solution, into droplets in the bottom of the container, within minutes if not seconds.
I wonder if that’s really true, because e.g. my TB20 POH recommends PRIST/EDME or IPA for flights in “humid” scenarios.
Note I am not talking about Avtur in which water definitely can and does exist in solution – see e.g. BA038.
I was taught to drain the tanks to check for water before moving the aircraft, as it may take a while for the water to resettle at the bottom and you may get a false negative when checking for water. Would be interested to hear how crucial this is. But even if it does settle out quickly, it could still presumably ice up fuel lines and benefit from anti-freeze.
Water settling out on the bottom of a tank should not block fuel lines because the fuel pickup is not from the very bottom. There is always some unusable fuel and that’s why.
At least that’s the theory!
However there are some “prob99 fuel icing” incidents e.g. a PA46 in France (2011 or so) which came all the way down from ~FL250 with the engine never restarting. Plus a Baron over the N Sea which had a double engine stoppage at ~FL200 over the N Sea and the engines didn’t restart till 2000ft (don’t know the date but I spoke to the pilot personally face to face; he bought a King Air immediately).
Also some pilots (myself included) have seen engine “hiccups” lasting a few seconds which while very rare definitely do exist. And I don’t think these are solid contamination because IMHO that would not just clear by itself. It should also not be gum (the stuff that forms in avgas tanks if standing for too long with an open air vent) because gum is soluble in avgas (and passes through normal filters).
From memory the buoyancy / viscosity ratios for water bubbles in avgas and air bubbles in water are similar. (Except the water goes down and the air goes up).
But just as the very finest air bubbles in water remain suspended for the longest time, I imagine the water/avgas bubble size is critical.
Why not try it out the next time you check the aeroplane?
When I did my PPL training I was curious whether it would form two distinctly visible layers so I put some Avgas in a drain tube and added some water. It clearly formed two distinct layers. After some shaking the layers were visible again very quickly.
I don’t think these experiments are rigorous enough.
Firstly, yes, it’s readily shown that if you pour a load of water into avgas, it “all” separates quickly. But that doesn’t mean that say 1% of it doesn’t remain in solution. You would need to do very careful experiments to check that.
Another thing is that I have never, in my 12 years of ownership of the TB20 from new, ever seen a single drop of water when I drain the tank drains or the fuel filter drain. Not the tiniest drop. But after a recent hiccup, when I drained all remaining fuel (26 USG), and sent about 2 litres of it to a test lab, they found small droplets of water in the bottom – the white specs here
Where did these come from? On that occasion, the plane was fuelled 3 days before the flight and I did drain the tanks and saw absolutely nothing, yet these doplets appared from apparently nowhere…
One possible explanation is that water can dissolve in avgas and remain suspended but will come out of solution (and form droplets which then remain as droplets from then on) if the fuel temperature falls at any time.
However, for water to freeze and block a fuel pipe, it isn’t necessary for it to come out of solution. As BA038 showed, with avtur, it can do this perfectly well while in solution.
But that doesn’t mean that say 1% of it doesn’t remain in solution
Would 1% remaining in the solution be a problem? I’d be surprised. Some combustion engine designs deliberately inject water into the combustion chamber. So the additional water would help cool your cylinders, allowing you to climb at VY to cruise level 
I can’t tell the size of the droplets visbible in the photo but they look very small to me. I can’t see how a few tiny droplets can cause a problem. Water injection has been used for a very long time to cool the intake charge of high powered engines to prevent detonation. If I remember correctly this can be more than 10% of the total fuel flow by volume which is a lot more than a few drops. The watertanks held tens of gallons in WWII engine installations.
Sure (about water injection into the combustion chamber) but if an engine stops due to water in the fuel it happens because the fuel path has become blocked (by ice or sludge), not because water has found its way into the combustion chamber.
Incidentally I am sure water injection systems have protection from the water in the tubing freezing, which it is guaranteed to do below 0C (exactly) 
The BA problem was caused by a filter. Interestingly the Meridian has a filter bypass if it gets blocked. The argument being that if the filter is restricting flow you would prefer unfiltered fuel instead of no fuel.
