We're starting to get into the areas where I hesitate to speak with any authority, as it's at the edges of what I know I know.
I do not think that the mixture would run lean. Assuming near total homogenation there would be a power and mileage loss, but the A/F mixture remaining in the combustion chamber would be roughly the same ratio as that which went out the exhaust valve.
That's my understanding at all. Assuming the charge is homogeneous (which may or may not be true), then charge going out the exhaust won't cause the engine to run lean.
If the homogenation process was less than successful then it could go slightly lean due to the fuel's greater inertia, but the various bends and turns in the flow path should result more in wetted surfaces than outright lost fuel.
You're assuming that the fuel injector is well upstream of the intake valve, and that the fuel remains in droplet form. Modern engine design strives to put the injector as close to the intake valve as possible. And the goal of fuel injector design is to make sure the fuel is vaporized, not remaining in droplet form.
However, with older engine designs, cold engines, or bad fuel, it can happen where the fuel sticks in liquid form to the intake port walls. However, it can't really build up to much extent as it would be just drawn out when the air rushes by. If this happened, it would come off the wall in large drop form, rather than mist, and thus more likely enter the combustion chamber in liquid form. That's bad, because there's a good chance it won't get burned completely, and then will go out the exhaust, still unburnt... so yeah, I guess you could "lose" that fuel.
In a newer, electronically controlled engine I can see this potentially being a real headache to program around.
I know my Pectel T2, no longer state of the art but is was about 10 years ago, I have an adjustment called "Injector End Angle". It's a 1D table just broken down into RPM ranges. The idea is, I believe, to have the injector close just before the intake valve. At low loads (and thus low injector on time) the injector on squirts fuel in the last bit of air column entering the combustion chamber. Therefore, any air that went out the exhaust port during valve overlap, would have no fuel in it. However, you can only cut it so close to the closing of the intake valve, so the fuel actually has time to travel with the column into the CC. If the valve closed before the fuel went in, the fuel would sit near the valve, and would likely go in at the start of the next intake event.
At high loads, the injector on-time can approach 80%, and injection end angle is pointless, since the injector is spraying fuel long before the intake valve opens.
You can imagine it would take a lot of dyno time to sort this out. I just left it on the default setting... for better or for worse. This is mostly an emissions thing. I just make up for any lost fuel with more injection time based on my reading from the O2.
12:1 isn't necessarily peak power. Assuming detonation isn't an issue, peak power is typically found at around 13.5:1. You just need a bit more fuel than air to make sure that every molecule of O2 that went into the CC finds some H or C to mate with. You don't want any more than that. However, in the real world, detonation is a problem. You need to balance that perfect chemical composition off against the increasing tendency to detonate. You could run 13.5:1, but would have to retard timing a lot to avoid detonation. Or, you could run rich, 11:1, with lots more timing. The actual peak power will be found somewhere between the two extremes. Again, lots of dyno time.
I just set mine for 13.5:1 at moderate loads (no detonation risk), 12:1 at heavier loads, and 11:1 under full boost. Timing is set to the detonation limit by ear, then backed off a bit. The resultant horsepower... well it is what it is. This is a fairly conservative way to tune.
And don't forget, detonation is most likely to happen at the peak torque point of the motor. You can lean it out a bit, or run more timing below and above. Lots of dyno time.
This is dyno time that a lot of people don't pay for. And if your tuner is aggressive to give you a big power number, without the investment to make sure it's safe... well that's why so many "tuner cars" go Kablouie!