Since the engine and majority of weight is now in the middle, the Corvair now becomes a mid engine car, which yes, does improve weight distribution. And as a mid engine car, you would find it more maneuverable to be sure. But also inherent to all mid engine cars with significant power (think your tony Italians from the late sixties to eighties) they also have a tendency to spin out very easily. Now I'm not saying that a stock Corvair was immune to such things, but by '65 the handling had become quite neutral.
Now I'm not saying that Ted Trevor's Crown Conversion Corvairs weren't cool (though I think his Corvair powered Manx Pikes Peak hill climber was cooler), I'm just saying that
I still think it would handle weird by comparison to a stock Corvair, which is a fine handling car.
True, if I were going for a rear engine vehicle, I'd rather have a Renault Turbo any day.