flat plate + extremely low viscosity fluid => nearly symmetric flow => nearly no Bernoulli => nearly no lift ?
Excellent question. The answer is no. Perhaps best explained by means of analogy.
If we balance a pencil vertically on its tip, does the direction in which it will fall "depend on gravity"? How can we answer that?
If we took the same pencil, on the same surface, to the moon (where the gravity is lower) would it fall in the same direction? The answer to this second question is, I hope, obviously "yes", as the magnitude of the vertical force makes no difference to the direction of fall. (Of course the rate of fall may depend on the magnitude of the vertical force, but the direction does not -- it depends on things like the mass distribution within the pencil, and the detailed shape of the tip, and the surface.)
If we took the same pencil, on the same surface, into outer space (where the gravity is zero) would it fall in the same direction? Well, with no gravity at all, the pencil would not fall, so the behaviour is quite different. We could legitimately say "no".
Does lift depend on viscosity? Well in the sense that absolutely zero viscosity would completely change the pattern of flow around the wing, yes. But all it takes is a tiny trace of viscosity (very high Reynolds Number) to create the flow pattern, and then the wing lifts as you'd expect. Increasing the viscosity will change the lift a little, but not much, even as the viscosity increases by orders of magnitude, and the lift actually tends to decrease as viscosity increases (Reynolds Number decreases).