Ian,
A propeller which doesn't feather won't necessarily "roll you over," but it can certainly be a contributing factor to a loss of control under the right circumstances.
In a light multi engine airplane with the engines on the wings (as opposed to say, a Cessna Skymaster, where both are on the fuselage), each engine produces thrust along a line which is parallel to, but separate from, the longitudinal axis of the airplane. If only one engine is running, the tendency is to want to push the airplane away from that engine. You can see the same tendency for yourself by standing upright and placing your arms straight out from your sides. Make a fist with each hand, each fist representing one engine of a multi-engine airplane (this example doesn't work so well if you have only one arm, and not at all if you have none, of course).
Have someone push on just one fist from behind (or pull on it from in front of you), and see if it doesn't try to twist you around. Of course it will...and it stands to reason that it won't if you have someone pushing on your fists equally on each side. Same for a multi engine airplane.
To prevent that twisting, or yawing motion, we have a rudder, of course. Unfortunately, the rudder can only do so much. At lower speeds, rudder authority is less, and at higher power settings on the "good" engine, the yawing moment is more. There comes a point at full power when the rudder isn't enough to prevent the airplane from yawing, and the airplane can depart controlled flight. The published speed at which this occurs is called "Vmc, or the point of minimum control with the critical engine inoperative, the operating engine at takeoff power, the aft-most center of gravity, maximum takeoff weight, flaps and cowl flaps set for takeoff, landing gear up, and a maximum of five degrees bank into the "good" engine. That's a lot to remember, but the main thing is that it's the speed at which directional control can no longer be maintained.
How the airplane departs controlled flight varies; it can be rapid, or a slow descending turn to a spin entry, a rollover, or it may simply start drifing in heading until the pilot either decreases angle of attack or most properly reduces power on the operating engine to maintain directional control.
Certain engine-propeller combinations produce a LOT of drag. In those cases, a propeller overspeed or loss of propeller control can indeed be a much greater force to the detrement of performance, than the operative engine. In fact, the operative engine may be the least of one's concerns. Such engines use several forms of overspeed protection, to include dedicated overspeed governors or more than one overspeed governor. These remove fuel from the engine as well as taking steps to control the propeller itself.
The engine that's critical is usually the one with the descending blade on it's propeller disc that's farthest from the fuselage. Tongue in cheek, I recently heard a Navajo pilot opine that his right engine was critical...because that's the one with the air conditioning on his airplane. He considered the loss of that engine much worse than any other calamity which might befall him.
The side of the propeller disc with the descending blade arguably is the side of the disc producing the greatest thrust (I say arguably because this isn't technically correct, but it's a great source for hangar arguments when it's a rainy day, and the topic for another thread). If you have two counter-rotating propellers where the descending blade is on the fuselage-side of theprop disc, then neither engine is critical. In light twins that have all propellers spinning counter-clockwise as seen from the cockpit, then the right engine is critical. The right engine produces a lesser assymetrical thrust situation than the left, so loss of the right puts the airplane in a more precarious condition. The reason for this is that assymetrical thrust yawing moment is greatest when the thrust line is farthest from the fuselage center line (picture the previous example of having someone push on your fists...this time have one person push on your fist, and the other your elbow...the fist is farther from your body, and though your assistants push equally as hard in both places, there's a greater moment on your fist...in this case we could say that your elbow is critical...because it's better to lose the pushing on your fist, than your elbow, and loss of pushing on the elbow puts you in a worse condition than loss of pushing on your fist).
Clear as mud? The opposite is true for clockwise spinning engines. In some cases, airplanes have been designed with the descending blade on both engines to the outside of the prop disc. The P-38 lightening is one example, making both engines "critical," or really neither more disadvantageous than the other...but making the loss of either one pretty darn bad. Certain of the Piper Aerostars were the same way, while others did just the opposite, with the descending blades on each engine on the fuselage-side...making neither engine critical (Piper Seneca is the same way).