Am I correct in saying that this would not require a gyro, just a 3 (2?) axis accelerometer, to detect pitch and roll, then adjust the ailerons and elevator to compensate?
No. The opposite is true. The accelerometer will be almost useless to detect rotations on a platform that's experiencing unknown accelerations. Your plane will be subject to two force vectors: gravity and lift+drag. Lift+drag will vary hugely as a function of the plane's pitch.
But here's a more general way you can know this is impossible, and you can use this method in many other cases than just IMUs. A sensor, or set of sensors gives you N values. You can't interpret this into a space with more than N dimensions.
A trivial example: You want a sensor to measure someone's position within a room. Would a single ultrasonic range finder be sufficient? No. A position in a room requires two values, (X, Y) coordinates. But an ultrasonic sensor gives you only one value, a length. There is no way to set up this sensor to solve your problem. But if you had two sensors, then it might be possible.
Now let's look at the plane. A non-accelerating plane is subject to one force only, gravity. The direction of gravity relative to the plane is a 3D vector, but luckily (if you're on Earth) you know its magnitude. That's 1 value, leaving 2 unknowns, so you could theoretically get away with a 2-axis accelerometer to make up those 2 unknowns and calculate the vector of gravity.
What about a plane in flight. Gravity and lift+drag are both 3D vectors, giving you 6 numbers. OK you know the magnitude of gravity, so 5 numbers. You'll need some kind of sensor that gives you at least 5 values. Therefore a 3-axis accelerometer cannot be enough.
While neither a 3-axis gyro nor a 3-axis accelerometer will be enough on their own, the gyro would be much more useful. This is because it's directly measuring rotations, which is the very thing you're trying to control.
Likewise, the accelerometer will be more useful for detecting and correcting deviations from travel in a straight line.