ORIGINAL: jester_s1
A lot of the answer to your question depends on what plane you are talking about. Some planes turn better with ailerons only than others do. The big limit you'll see by not having a rudder is you can't handle nearly as much wind. When turning from upwind to downwind, the wind pushes your tail out of the turn, forcing you to roll nearly sideways and use the elevator to get through. That works, but it makes for such nicer turns (and far less stall prone) to be able to horse it around with the rudder.
Gusts can do what you describe as can turbulence, but a turn from upwind to downwind will not affect the plane in any way. The amount of wind makes no difference unless you have to land and T.O. in a certain direction forcing a crosswind landing. Rudder does not help avoid a stall, but can make the stall less likely to develop into a spin. The key to flying a plane without rudder is to keep the speed up and T.O. and land into the wind. Aircraft designed to fly without a rudder will tend to have a larger vertical surface and some washout in the wings to increase low speed stability. Aileron differential is also advisable.