If oil in a frying pan gets displaced, say by too much liquid being sweated, will the meat be unevenly cooked?
Not in my experience. The water will spread out through the pan and meat will still cook evenly, just slower.  You shouldn't have this problem with most meats, but it can be a problem with chicken breasts in particular, and if you also have vegetables in the pan they can release a fair amount of water.

The basic problem with too much water releasing from meat (or anything else) when frying is that it reduces the temperature of the oil down to the boiling point of water. That kills the advantage oil has over water, that it's boiling point is much higher. (Higher in fact than the temperatures typically used in cooking. The bubbling you see when frying are caused by the vaporization of water.) That's what oil makes more efficient at heat transfer, it's temperature is higher.  This also means that it still should cook evenly, just slower, because the oil will be at the same temperature as the water. You're basically just simmering the meat instead of frying it. 

When this happens the simple solution is to temporarily turn up the heat. It takes a lot more energy to convert water into steam than it does to keep oil alone at a desired cooking temperature. You won't have to worry about burning anything, because the water in the pan will automatically regulate the temperature, keeping it at or below 100 C (212 F). Once enough of the water has been evaporated you'll start to hear normal frying sounds again and you can turn back the heat to normal.