Lets say a quadrocopter's rotors are 2 feet apart, and 2 feet beneath it is attached a symmetrical, balanced payload that was x feet wide (with space for air from the rotors to move through) - if the rotors are powerful enough, would it still be somewhat controllable laterally if x was greater than 2 feet, or would that configuration ruin all ability to control regardless of the rotors' power?
While the payload will affect contols (as each payload do) with enough powerful rotors it will be controlablle.
We know, that quadrocopter with rotors inside rings is contollable. Even if you make those ring longer, it would be still controllable. Even if those rigs are long pipes, it would be still controllable. And even if those pipes are bend to sides, it would be still controllable.
So if you put the payload well down under the bend pipes, it would be still controlable. And so you even do not need such rings/pipes.
There will be problem with the weight, with wind moving the payload, if the payload is near the rotors, then it will be harder to control and would need more power, but while the rotors can pull air from above with enough force (and dispose the air somehow, just to be able pull more of air from above) it would be controllable. Maybe you would need computer for fast response to make that stable, but this is just technicality, not principaial problem.
Also another view: imegine, that you have 100 m long rope (as for flying kite) and attach it under the quad, then fly it up - it will be contollable ofc. Even when it reach the rope limit, it could be contolled to take nearly any position on the half-spere allowed by the rope.
If the rotor would be powerfull, it would take you to the air. If you fix it to the ground, then if would still be controllable, just not able to lift whole Earth. But if you attach it to really big desk, it would lift such desk up.
Even if you would attach it to really wide payload (like parachute under it) it would be controllable on the 100m rope for sure. Also on 99m, 98m and so .. as the rope would be shorter (like 10, 5, 2, 1m), it would be harder to make it fly in stable manners, but it would be still controllable.
So it is just function of rotor power and controller speed of reactions.
The quad works such, that if takes air from above, climbing inside it as a srew to nut. The rocket (on the other hand - it is opposite) works such, that it put weight fast under it (the burned gas) - so rocket may not be able pull wide payload under it, but would be able push wide load above it.